Article
Mathematics, Applied
Tim Ophelders, Roel Lambers, Frits C. R. Spieksma, Tjark Vredeveld
Summary: For any complete graph with at least 6 vertices, there exists an equitable Hamiltonian cycle that can be decomposed into two perfect matchings.
DISCRETE APPLIED MATHEMATICS
(2021)
Article
Mathematics, Applied
Ran Gu, Hui Lei, Yongtang Shi, Yiqiao Wang
Summary: This paper discusses the existence of rainbow-free coloring in random k-uniform hypergraphs, and provides the threshold function and the answer.
DISCRETE APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Daniel W. Cranston, Michael Lafferty, Zi-Xia Song
Summary: An odd coloring of a graph is defined as a color assignment in which every non-isolated vertex has at least one color that appears an odd number of times in its neighborhood. It has been shown that every planar graph can be odd 9-colored, and it is conjectured that every planar graph can be odd 5-colored. This conjecture has been confirmed for planar graphs of girth at least seven and outerplanar graphs. Furthermore, it has been proven that every planar graph can be odd 8-colored. In this study, we prove that every 1-planar graph can be odd 23-colored, where a graph is 1-planar if it can be drawn in the plane with each edge crossed by at most one other edge.
DISCRETE APPLIED MATHEMATICS
(2023)
Article
Development Studies
Rachel S. Friedman, Kerrie A. Wilson, Jonathan R. Rhodes, Elizabeth A. Law
Summary: This study further develops our understanding of distributional equity by examining community-based forest management in Indonesia and comparing changes under different distributional norms. The results demonstrate the importance of defining fair and just distributions to meet equity objectives.
Article
Mathematics, Applied
Peter Bradshaw
Summary: Given a family g of graphs spanning a common vertex set V, a cooperative coloring of g is a collection of one independent set from each graph G E g such that the union of these independent sets equals V. We prove that for large d, there exists a family g of (1 + o(1))log d no cooperative coloring, which significantly improves a result of Aharoni, Berger, Chudnovsky, Havet, and Jiang (Electronic Journal of Combinatorics, 2020). Our family g consists entirely of star forests, and we show that this value for lgl is asymptotically best possible in the case that g is a family of star forests.
ELECTRONIC JOURNAL OF COMBINATORICS
(2023)
Article
Mathematics
Jeffrey A. Mudrock, Max Marsh, Tim Wagstrom
Summary: The paper discusses the concept of list equitable coloring and verifies the related conjecture, focusing on the equitable k-choosability of graphs as the main research topic.
DISCUSSIONES MATHEMATICAE GRAPH THEORY
(2021)
Article
Mathematics, Applied
Hong-Jian Lai, Lucian Mazza
Summary: The concept of abelian group colorings as the dual concept of group connectivity of graphs was introduced by Jaeger et al. A recent study by HuI'sek, Moheln{\i}\'kov\'a, and SI'\'amal found examples of Z4-connected but not Z22-connected graphs, and vice versa, raising unanswered questions in the group coloring problem. The extension of group coloring to non-abelian groups was discussed by Li and Lai, introducing the concept of a group coloring local structure.
SIAM JOURNAL ON DISCRETE MATHEMATICS
(2021)
Article
Mathematics
Adi Jarden, Ziv Shami
Summary: This passage discusses the connections between the existence of homogeneous sets for certain edge colorings and the existence of branches in certain trees. As a result, it is shown that any locally additive coloring of a cardinal kappa has a homogeneous set of size kappa, provided that the number of colors mu satisfies mu+<^>+<kappa$. Another result states that an uncountable cardinal kappa is weakly compact if and only if kappa is regular, has the tree property, and for every lambda, mu*<kappa$ such that every tree of height mu with lambda nodes has less than kappa*$\kappa <^>*$ branches.
MATHEMATICAL LOGIC QUARTERLY
(2022)
Article
Mathematics
Jeffrey A. Mudrock, Madelynn Chase, Ezekiel Thornburgh, Isaac Kadera, Tim Wagstrom
Summary: The equitable choosability of complete bipartite graphs was studied, leading to conclusions and results for certain conditions under which the graphs are equitably choosable.
DISCUSSIONES MATHEMATICAE GRAPH THEORY
(2021)
Article
Mathematics
Mirko Petrusevski, Riste Skrekovski
Summary: The main aim of the article is to study a coloring notion for digraphs, known as an odd k-edge coloring. It is proven that it can be decided in polynomial time whether a digraph admits an odd 2-edge coloring. The paper also poses several conjectures, questions, and open problems related to this coloring notion.
Article
Mathematics
N. Bazhenov, N. Greenberg, A. Melnikov, R. Miller, K. M. Ng
Summary: The article discusses the concepts of alpha-coloring and distinguishing in structures, and proves that computing the distinguishing number of a structure can be very challenging. It also shows that computable Boolean algebras have a specific distinguishing 2-coloring feature, and introduces a new concept of computable distinguishing 2-coloring in separable spaces.
LOBACHEVSKII JOURNAL OF MATHEMATICS
(2021)
Editorial Material
Chemistry, Multidisciplinary
Anne Pichon
Summary: The article discusses the entrenched inequalities in the research community and the role of funders in replacing privilege with equitable and transparent systems.
Article
Mathematics, Applied
Xinmiao Zhang, Yirong Guo, Xia Zhang
Summary: This paper studies a class of plane graphs and provides a lower bound for their polychromatic number, improving a known lower bound in certain cases.
DISCRETE MATHEMATICS ALGORITHMS AND APPLICATIONS
(2022)
Article
Mathematics, Applied
Anna Bachstein, Wayne Goddard, Michael A. Henning, John Xue
Summary: This article introduces the concept of P-compelling coloring, discusses its applications in graph theory, generalizes multiple related chromatic numbers, and provides some general bounds and algorithmic results.
APPLIED MATHEMATICS AND COMPUTATION
(2022)
Article
Mathematics, Applied
Wei Yang, Baoyindureng Wu
Summary: This paper investigates the edge weight problem and the concept of S-packing edge-coloring in graphs. A series of conclusions about packing edge-colorings are proved and the previous related research results are strengthened.
APPLIED MATHEMATICS AND COMPUTATION
(2022)
Article
Mathematics, Applied
Sheng-Hua Chen, Gerard Jennhwa Chang
DISCRETE APPLIED MATHEMATICS
(2015)
Article
Mathematics
Gerard J. Chang, Sheng-Hua Chen, Chi-Yun Hsu, Chia-Man Hung, Huei-Ling Lai
DISCRETE MATHEMATICS
(2015)
Article
Mathematics
Hsiang-Chun Hsu, Gerard Jennhwa Chang
GRAPHS AND COMBINATORICS
(2016)
Article
Computer Science, Software Engineering
Ching-Chi Lin, Gen-Huey Chen, Gerard J. Chang
Article
Mathematics, Applied
Wu-Hsiung Lin, Gerard J. Chang
DISCRETE APPLIED MATHEMATICS
(2013)
Article
Mathematics, Applied
Bo-Jr Li, Gerard Jennhwa Chang
DISCRETE APPLIED MATHEMATICS
(2014)
Article
Mathematics, Applied
James K. Lan, Gerard Jennhwa Chang
DISCRETE APPLIED MATHEMATICS
(2014)
Article
Computer Science, Interdisciplinary Applications
Gerard Jennhwa Chang, Ma-Lian Chia, David Kuo, Ji-Yin Lin, Jing-Ho Yan
JOURNAL OF COMBINATORIAL OPTIMIZATION
(2014)
Article
Computer Science, Interdisciplinary Applications
Hsiang-Chun Hsu, Gerard Jennhwa Chang
JOURNAL OF COMBINATORIAL OPTIMIZATION
(2014)
Article
Computer Science, Interdisciplinary Applications
Gerard Jennhwa Chang, Nicolas Roussel
JOURNAL OF COMBINATORIAL OPTIMIZATION
(2015)
Article
Mathematics
Gerard Jennhwa Chang, N. Narayanan
JOURNAL OF GRAPH THEORY
(2013)
Article
Mathematics, Applied
Gerard Jennhwa Chang, Jephian Chin-Hung Lin
LINEAR ALGEBRA AND ITS APPLICATIONS
(2014)
Article
Mathematics, Applied
Gerard Jennhwa Chang, Keqin Feng, Liang-Hao Huang, Mei Lu
LINEAR ALGEBRA AND ITS APPLICATIONS
(2014)
Article
Mathematics
Gerard Jennhwa Chang, Mickael Montassier, Arnaud Pecher, Andre Raspaud
DISCUSSIONES MATHEMATICAE GRAPH THEORY
(2014)
Article
Mathematics, Applied
Valentin Borozan, Gerard Jennhwa Chang, Nathann Cohen, Shinya Fujita, Narayanan Narayanan, Reza Naserasr, Petru Valicov
ELECTRONIC JOURNAL OF COMBINATORICS
(2015)
Article
Mathematics
Jozsef Balogh, Ce Chen, Grace Mccourt, Cassie Murley
Summary: This article studies the case of small cliques in the Ramsey-Turan number RT(n, H, f(n)), and proves that these cliques have phase transitions under certain conditions using mathematical methods.
EUROPEAN JOURNAL OF COMBINATORICS
(2024)
Article
Mathematics
Peter Frankl, Jian Wang
Summary: In this paper, it is proven that for n > 36k, any intersecting family F subset of (((k))([n])) has a diversity of at most ((n-3)(k-2)), improving upon the previous best bound n > 72k.
EUROPEAN JOURNAL OF COMBINATORICS
(2024)
Article
Mathematics
Malgorzata Bednarska-Bzdega
Summary: This article introduces the Ramsey game played on the edge set of K-N and investigates the online Ramsey number. The research finds that when the number of vertices k is less than n and n approaches infinity, the upper bound of the number of rounds in the game is (5/3 + o(1))n. Furthermore, it is proven that when n≥10, the upper bound of the number of rounds in the game is [7n/5] - 1, improving the previous result obtained by J. Cyman, T. Dzido, J. Lapinskas, and A. Lo and verifying their conjecture (r) over tilde (P-4, P-n) = [7n/5] - 1.
EUROPEAN JOURNAL OF COMBINATORICS
(2024)
Article
Mathematics
Samantha L. Dahlberg, Hemanshu Kaul, Jeffrey A. Mudrock
Summary: DP-coloring is a generalization of list coloring that calculates the minimum number of DP-colorings in a graph's cover. This paper presents a new approach to compute the DP-coloring number and provides improved bounds compared to existing methods. It also proves that the DP-color function is not chromatic adherent.
EUROPEAN JOURNAL OF COMBINATORICS
(2024)
Article
Mathematics
Donggyu Kim, Sang-il Oum
Summary: The article explores the essential properties of prime graphs and provides conditions for the existence of non-essential vertices. The research findings are of significant importance for understanding the structure and properties of graphs.
EUROPEAN JOURNAL OF COMBINATORICS
(2024)
Article
Mathematics
Adam Gowty, Daniel Horsley, Adam Mammoliti
Summary: This article determines the minimum value of a family F, denoted as |F-up down arrow|, as a function of the size of the ground set and the family itself. It solves the isoperimetric problem on a graph and provides insights into the isoperimetric problem for hypercubes. Additionally, it has implications for the study of cross-Sperner families.
EUROPEAN JOURNAL OF COMBINATORICS
(2024)
Article
Mathematics
Shun-ichi Maezawa
Summary: This paper discusses the definition and properties of k-linked graphs and refers to previous research results. It improves these results by considering the graph obtained from deleting edges as a minor.
EUROPEAN JOURNAL OF COMBINATORICS
(2024)
Article
Mathematics
Ming-Zhu Chen, A-Ming Liu, Xiao-Dong Zhang
Summary: In this paper, a sharp upper bound for the spectral radius of an n-vertex F-minor-free graph is presented, and the graphs that achieve this bound are characterized. This result is of significant importance in the field of mathematics.
EUROPEAN JOURNAL OF COMBINATORICS
(2024)
Article
Mathematics
Noga Alon
Summary: This study discusses the problem of fixed graph H with an even number of edges and explores the properties of D-H(n) and possible upper bounds.
EUROPEAN JOURNAL OF COMBINATORICS
(2024)
Article
Mathematics
Yan Wang
Summary: We prove that for any integer t >= 2, every properly edge colored n-vertex graph with average degree at least (log n)2+o(1) contains a rainbow subdivision of a complete graph of size t. This result is within a (log n)1+o(1) factor of the lower bound, and also implies a result on the rainbow Turan number of cycles.
EUROPEAN JOURNAL OF COMBINATORICS
(2024)
Article
Mathematics
Xiaoyu He, Emily Huang, Ihyun Nam, Rishubh Thaper
Summary: In this paper, we study the sizes of shuffle squares and reverse shuffle squares, and confirm a conjecture about the size of shuffle squares. We also disprove a conjecture about the size of reverse shuffle squares. When the alphabet size is small, we separately study the binary case.
EUROPEAN JOURNAL OF COMBINATORICS
(2024)
Article
Mathematics
Gergely Ambrus, Martin Balko, Nora Frankl, Attila Jung, Marton Naszodi
Summary: This article discusses the Helly numbers of a class of exponential lattices and provides their exact values in some instances. A problem is solved and a characterization of exponential lattices with finite Helly numbers is given.
EUROPEAN JOURNAL OF COMBINATORICS
(2024)
Article
Mathematics
Michael Ren
Summary: Building on the recent work of Garg and Peng, this article continues the investigation into classical and consecutive pattern avoidance in rooted forests. The authors prove a forest analogue of the Stanley-Wilf conjecture for avoiding a single pattern and certain other sets of patterns. Their analytic techniques easily generalize to different types of pattern avoidance and allow for computations of convergent lower bounds of the forest Stanley-Wilf limit. The article concludes with several open questions and directions for future research, including some on the limit distributions of certain statistics of pattern-avoiding forests.
EUROPEAN JOURNAL OF COMBINATORICS
(2024)
Article
Mathematics
Hyobeen Kim, Jae-baek Lee, Mark Siggers
Summary: This article discusses the complexity of the Mix(H) and NonFlat(H) problems. If the given graph H is triangle-free and reflexive, with at least one cycle, then Mix(H) is coNP-complete. We also prove that for any reflexive graph H, if the clique complex H of H has a free, nontrivial homology group H1(H), then NonFlat(H) is NP-complete.
EUROPEAN JOURNAL OF COMBINATORICS
(2024)
Article
Mathematics
Mahya Ghandehari, Jeannette Janssen
Summary: This passage introduces the Gamma function on graphons, which aims to measure the extent to which a graphon exhibits the Robinson property. Robinson graphons are a model for graphs with a natural line embedding, where most edges are local. The passage discusses the compatibility of the Gamma function with the cut norm and the convergence conditions for graph sequences.
EUROPEAN JOURNAL OF COMBINATORICS
(2024)
