Results 41 to 50 of about 38,199 (317)
Total Coloring of Claw-Free Planar Graphs
Discussiones Mathematicae Graph Theory, 2022 A total coloring of a graph is an assignment of colors to both its vertices and edges so that adjacent or incident elements acquire distinct colors. Let Δ(G) be the maximum degree of G.
Liang Zuosong
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From light edges to strong edge-colouring of 1-planar graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 A strong edge-colouring of an undirected graph $G$ is an edge-colouring where every two edges at distance at most~$2$ receive distinct colours. The strong chromatic index of $G$ is the least number of colours in a strong edge-colouring of $G$.
Julien Bensmail +3 more
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Planar Transitive Graphs [PDF]
The Electronic Journal of Combinatorics, 2018 We prove that the first homology group of every planar locally finite transitive graph $G$ is finitely generated as an $\Aut(G)$-module and we prove a similar result for the fundamental group of locally finite planar Cayley graphs. Corollaries of these results include Droms's theorem that planar groups are finitely presented and Dunwoody's theorem that
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Testing hereditary properties of nonexpanding bounded-degree graphs [PDF]
, 2007 We study graph properties that are testable for bounded-degree graphs in time independent of the input size. Our goal is to distinguish between graphs having a predetermined graph property and graphs that are far from every graph having that property. It
Christian Sohler +5 more
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The complexity of two graph orientation problems
, 2012 This is the post-print version of the Article. The official published version can be accessed from the link below - Copyright @ 2012 ElsevierWe consider two orientation problems in a graph, namely the minimization of the sum of all the shortest path ...
Noble, Steven D. +7 more
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An algorithm of graph planarity testing and cross minimization [PDF]
Computer Science Journal of Moldova, 2007 This paper presents an overview on one compartment from the graph theory, called graph planarity testing. It covers the fundamental concepts and important work in this area.
Vitalie Cotelea, Stela Pripa
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On planar hypohamiltonian graphs
Journal of Graph Theory, 2010 Summary: We present a planar hypohamiltonian graph on 42 vertices and (as a corollary) a planar hypotraceable graph on 162 vertices, improving the bounds of Zamfirescu and Zamfirescu and show some other consequences. We also settle the open problem whether there exists a positive integer \(N\), such that for every integer \(n\geq N\) there exists a ...
Wiener, Gabor, Araya, Makoto
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On Computation of Degree-Based Entropy of Planar Octahedron Networks
Journal of Function Spaces, 2022 Chemical graph theory is the combination of mathematical graph theory and chemistry. To analyze the biocompatibility of the compounds, topological indices are used in the research of QSAR/QSPR studies.
Tian-Le Sun +5 more
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Molecular Oncology, EarlyView.Patient‐derived organoids (PDOs) from pancreatic, colorectal, and gastric cancers were used to evaluate standard and experimental therapies. Incorporating cancer‐associated fibroblasts (CAFs) into organoid cultures improved patient therapy outcome prediction.
Marcin Grochowski +12 more
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Treewidth 2 in the Planar Graph Product Structure Theorem [PDF]
Discrete Mathematics & Theoretical Computer ScienceWe prove that every planar graph is contained in $H_1\boxtimes H_2\boxtimes K_2$ for some graphs $H_1$ and $H_2$ both with treewidth 2. This resolves a question of Liu, Norin and Wood [arXiv:2410.20333]. We also show this result is best possible: for any
Marc Distel +4 more
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