Article
Mathematics, Applied
Samir Shukla
Summary: This paper investigates the Vietoris-Rips complex in a metric space and determines its nontrivial reduced homology dimensions. It also discusses the collapsibility and collapsibility number of the complex.
SIAM JOURNAL ON DISCRETE MATHEMATICS
(2023)
Article
Mathematics
Greg Malen
Summary: This paper proves a sufficient condition for a finite clique complex to collapse to a k-dimensional complex and demonstrates thresholds for (k + 1)-collapsibility in a sparse random clique complex. Specifically, if every strongly connected, pure (k + 1)-dimensional subcomplex of a clique complex X has a vertex of degree at most 2k + 1, then X is (k + 1)-collapsible. In the random model X(n, p) of clique complexes of an Erdos-Renyi random graph G(n, p), it is shown that for any fixed k = 0, if p = n(-a) for fixed a > 1/(k +1), then a clique complex X =(dist) X(n, p) is (k + 1)-collapsible with high probability.
DISCRETE MATHEMATICS
(2023)
Article
Mathematics, Applied
Jian Lu, Xiang-Feng Pan, Huiqing Liu
Summary: This paper investigates the relationship between cover cost and other graph invariants in bicyclic graphs, provides sharp bounds for CCG(x) among all bicyclic graphs, and characterizes the corresponding extremal graphs.
APPLIED MATHEMATICS AND COMPUTATION
(2021)
Article
Mathematics
Yusuf Civan
Summary: We prove the existence of a connected graph H-k for every integer k >= 1, such that the number of vertices v(H-k) is equal to the regularity reg(H-k) plus k.
JOURNAL OF ALGEBRAIC COMBINATORICS
(2023)
Article
Mathematics
Wahyuni Abidin, Anm Salman, Suhadi Wido Saputro
Summary: This paper studies the properties of resolving sets and metric dimension in graphs, and provides a method for calculating the non-isolated resolving number of a graph. Additionally, the concepts of corona product graph and regular graph are introduced, along with corresponding calculation formulas.
Article
Mathematics
Zemin Jin, Yumiao Shi, Shujing Wang, Xueyao Gui
Summary: This paper examines various costs and indices of dumbbell graphs B-n (p, l, q), provides explicit formulas for them, and determines the corresponding extremal graphs.
BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY
(2023)
Article
Automation & Control Systems
Jiaqi Gu, Ping Guo
Summary: The PEAF algorithm framework consists of preprocessing, solving, and inverse-processing stages, while the PEAVC solver improves algorithm performance using various methods and achieves outstanding results.
ENGINEERING APPLICATIONS OF ARTIFICIAL INTELLIGENCE
(2021)
Article
Engineering, Geological
Shuai Shao, Shengjun Shao, Jun Li, Dandan Zhu
Summary: There is a lot of new traffic engineering construction on the loess plateau, presenting challenges for tunnel stability. Current methods for evaluating loess collapsibility are inaccurate and time-consuming, but a new in situ sand well water seepage saturated loess test method has been proposed as a more efficient solution.
ENGINEERING GEOLOGY
(2021)
Article
Materials Science, Multidisciplinary
Vaclav Merta, Jaroslav Beno, Tomas Obzina, Filip Radkovsky, Ivana Kroupova, Petr Lichy, Martin Folta, Kamila Janovska, Isabel Nguyenova, Miroslav Dostal
Summary: The study aims to evaluate the parameters of core mixtures using different binder systems in order to assess their influence on the surface requirements and product quality of castings. The research compares the advantages and disadvantages of organically bonded cores with inorganically bonded cores to potentially reduce the environmental impact of industrial production.
Article
Computer Science, Information Systems
Huiqing Liu, Jian Lu, Shunzhe Zhang, Xiuyu Zhong
Summary: This paper discusses the problem of path cover in connected quasi-claw-free graphs with independent sets having minimum degree sum, providing sharp conditions for the path cover number.
Article
Mathematics
Parthajit Bhowal, Deiborlang Nongsiang, Rajat Kanti Nath
Summary: This paper studies various properties of the non-solvable graph NSG of a group, including vertex degree, domination number, independence number, etc. It also compares the properties of two groups G and H with isomorphic non-solvable graphs, and concludes by showing that NSG does not fit into five specific geometric structures.
BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY
(2022)
Article
Engineering, Civil
Yongguo Yao, Yuchuan Zhang, Xulong Gao, Hongwei Huang, Dongfa Liu, Xinqin Hui
Summary: The study revealed different permeability and collapsibility characteristics of sandy loess under simulated rainfall and saturated infiltration conditions, with crack development experiencing multiple stages and limited lateral water migration. Collapse deformation was most pronounced near the test pit boundary, with rainfall-induced deformation being only 11.6% of that from saturated infiltration. Activation of sandy loess collapsibility requires both specific moisture content variations and sustained moisture states.
JOURNAL OF HYDROLOGY
(2021)
Editorial Material
Polymer Science
Alexander S. Novikov
Summary: Non-covalent interactions are a key topic in modern chemical science, with significant effects on the properties of polymers. This Special Issue collects fundamental and applied research papers focused on non-covalent interactions in polymer chemistry and related fields, including original research articles and comprehensive review papers. The scope of the Special Issue is broad, welcoming contributions on the synthesis, structure, functionality, and properties of polymer systems involving non-covalent interactions.
Article
Mathematics, Applied
Rashid Farooq, Laiba Mudusar
Summary: The eccentricity e(w) of a vertex w in a molecular graph G is the maximum distance of w from any other vertex of G; The non-self-centrality number (NSC) of a graph G is defined by N(G) = Sigma(w not equal z) vertical bar e(w) - e(z)vertical bar, where summation goes over all the unordered pairs of vertices of G; This paper determines the non-self-centrality number of TUC4C8 and V-phenylenic nanotubes.
Article
Mathematics, Applied
Thomas Magnard, Michael Skotnica, Martin Tancer
Summary: This paper explores the removal-collapsibility condition of pure simplicial complexes and its higher-dimensional generalization. By introducing star decomposability, it is shown that the second barycentric subdivision of a simplicial complex satisfying certain conditions exhibits shellability.
SIAM JOURNAL ON DISCRETE MATHEMATICS
(2021)
Article
Computer Science, Interdisciplinary Applications
Ilkyoo Choi, Jinha Kim, Minki Kim
JOURNAL OF COMBINATORIAL OPTIMIZATION
(2019)
Article
Mathematics, Applied
Gi-Sang Cheon, Jinha Kim, Minki Kim, Sergey Kitaev
DISCRETE APPLIED MATHEMATICS
(2019)
Article
Mathematics, Applied
Ilkyoo Choi, Jinha Kim
DISCRETE APPLIED MATHEMATICS
(2020)
Article
Mathematics
Jinha Kim, Ryan R. Martin, Tomas Masarik, Warren Shull, Heather C. Smith, Andrew Uzzell, Zhiyu Wang
EUROPEAN JOURNAL OF COMBINATORICS
(2020)
Article
Mathematics, Applied
Jinha Kim, Minki Kim, O-joung Kwon
Summary: This paper studies rainbow independent sets in graphs and identifies two dense graph classes that satisfy a specific property.
DISCRETE APPLIED MATHEMATICS
(2022)
Article
Mathematics
Jinha Kim, Minki Kim
Summary: This paper examines the homological properties of the noncover complexes of hypergraphs and obtains an upper bound on their Leray numbers in terms of hypergraph domination numbers. The proof idea is also applied to compute the homotopy type of noncover complexes of certain uniform hypergraphs, extending known results on graphs.
JOURNAL OF COMBINATORIAL THEORY SERIES A
(2021)
Article
Mathematics
Ron Aharoni, Joseph Briggs, Jinha Kim, Minki Kim
Summary: Drisko proved the existence of rainbow matching in bipartite graphs and speculated about its sufficiency in general graphs. The conjecture is known as badges and has been improved from 3n-2 to 3n-3. A cooperative generalization was also provided for sets of edges containing a matching of size n.
DISCRETE MATHEMATICS
(2021)
Article
Mathematics
Jinha Kim, Minki Kim, O-Joung Kwon
Summary: The study proves the existence of a certain integer relation on the plane, allowing for the discovery of disjoint segments satisfying specific conditions for a given set of vectors and families of line segments.
DISCRETE MATHEMATICS
(2021)
Article
Mathematics, Applied
Ron Aharoni, Joseph Briggs, Minho Cho, Jinha Kim
Summary: This paper studies the problem of F-rainbow matching in bipartite graphs. By analyzing the union of k members, it is proved that when the union contains a matching of size n, there exists an F-rainbow matching of size n. Furthermore, it is also shown by topological and combinatorial arguments that the result holds for k = 1.
ELECTRONIC JOURNAL OF COMBINATORICS
(2022)
Article
Mathematics
Jinha Kim
Summary: This study proves Engstrom's conjecture about the independence complex of graphs with no induced cycle of length divisible by 3. The result shows that the complex is either contractible or homotopy equivalent to a sphere. This strengthens previous research and verifies related conjectures, while also solving a weaker conjecture.
EUROPEAN JOURNAL OF COMBINATORICS
(2022)
Article
Mathematics
Eun-Kyung Cho, Jinha Kim, Minki Kim, Sang-il Oum
Summary: An independent dominating set, also known as a maximal independent set, in a graph is a set of non-adjacent vertices such that every non-included vertex is adjacent to at least one vertex in the set. We prove that for graphs with maximum degree at most 4 or greater than or equal to 6, every connected graph with n vertices has an independent dominating set of size at most (1 - [Delta 2/4]+Delta )(n - 1) + 1. We also characterize the connected graphs that achieve equality and show that other connected graphs have an independent dominating set of size at most (1 -Delta/Delta(2)/4]+Delta )n.
JOURNAL OF COMBINATORIAL THEORY SERIES B
(2023)
Article
Mathematics, Applied
Debsoumya Chakraborti, Jaehoon Kim, Jinha Kim, Minki Kim, Hong Liu
Summary: This paper studies regular graphs in which random walks starting from a positive fraction of vertices have small mixing time. It is proven that such graphs are virtually expanders and do not have small separators, answering a question raised by Pak. As a result, it is also shown that sparse regular graphs with many well-mixing vertices have long cycles, and these cycles can be found in polynomial time. Furthermore, it is demonstrated that if the random walks from a positive fraction of vertices are well-mixing, then the random walks from almost all vertices are also well-mixing, although with slightly worse mixing time.
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
(2022)
Article
Mathematics, Applied
Gi-Sang Cheon, Jinha Kim, Minki Kim, Sergey Kitaev, Artem Pyatkin
JOURNAL OF COMBINATORICS
(2019)