Results 21 to 30 of about 1,442,532 (348)
Planar Graphs as VPG-Graphs [PDF]
Journal of Graph Algorithms and Applications, 2013 A graph is Bk-VPG when it has an intersection representation by paths in a rectangular grid with at most k bends (turns). It is known that all planar graphs are B3-VPG and this was conjectured to be tight. We disprove this conjecture by showing that all planar graphs are B2-VPG.
Steven Chaplick, Torsten Ueckerdt
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On the planarity of line Mycielskian graph of a graph
Ratio Mathematica, 2020 The line Mycielskian graph of a graph G, denoted by Lμ(G) is defined as the graph obtained from L(G) by adding q+1 new vertices E' = ei' : 1 ≤ i ≤ q and e, then for 1 ≤ i ≤ q , joining ei' to the neighbours of ei and to e.
Keerthi G. Mirajkar +1 more
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The Electronic Journal of Combinatorics, 2019 We say that a graph $H$ is planar unavoidable if there is a planar graph $G$ such that any red/blue coloring of the edges of $G$ contains a monochromatic copy of $H$, otherwise we say that $H$ is planar avoidable. That is, $H$ is planar unavoidable if there is a Ramsey graph for $H$ that is planar. It follows from the Four-Color Theorem and a result of
Axenovich, M. +3 more
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The maximum number of pentagons in a planar graph [PDF]
Journal of Graph Theory, 2019 In 1979, Hakimi and Schmeichel considered the problem of maximizing the number of cycles of a given length in an n $n$ ‐vertex planar graph. They precisely determined the maximum number of triangles and four‐cycles and presented a conjecture for the ...
E. Györi +4 more
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A bipartite graph associated to elements and cosets of subgroups of a finite group
AIMS Mathematics, 2021 Let $ G $ be a finite group. A bipartite graph associated to elements and cosets of subgroups of $ G $ is the simple undirected graph $ \Gamma(G) $ with the vertex set $ V(\Gamma(G)) = A\cup B $, where $ A $ is the set of all elements of a group $ G ...
Saba Al-Kaseasbeh, Ahmad Erfanian
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Popular Conjectures as a Barrier for Dynamic Planar Graph Algorithms [PDF]
IEEE Annual Symposium on Foundations of Computer Science, 2016 The dynamic shortest paths problem on planar graphs asks us to preprocess a planar graph G such that we may support insertions and deletions of edges in G as well as distance queries between any two nodes u, v subject to the constraint that the graph ...
Amir Abboud, Søren Dahlgaard
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Equitable Coloring of IC-Planar Graphs with Girth g ≥ 7
Axioms, 2023 An equitable k-coloring of a graph G is a proper vertex coloring such that the size of any two color classes differ at most 1. If there is an equitable k-coloring of G, then the graph G is said to be equitably k-colorable.
Danjun Huang, Xianxi Wu
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Planar Graph Perfect Matching Is in NC [PDF]
IEEE Annual Symposium on Foundations of Computer Science, 2017 Is perfect matching in NC? That is, is there a deterministic fast parallel algorithm for it? This has been an outstanding open question in theoretical computer science for over three decades, ever since the discovery of RNC matching algorithms.
Nima Anari, V. Vazirani
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The Electronic Journal of Combinatorics, 2018 A nonplanar graph $G$ is called almost-planar if for every edge $e$ of $G$, at least one of $G\backslash e$ and $G/e$ is planar. In 1990, Gubser characterized 3-connected almost-planar graphs in his dissertation. However, his proof is so long that only a small portion of it was published.
Guoli Ding +2 more
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Discussiones Mathematicae Graph Theory, 2023 DP-coloring is generalized via relaxed coloring and variable degeneracy in [P. Sittitrai and K. Nakprasit, Su cient conditions on planar graphs to have a relaxed DP-3-coloring, Graphs Combin. 35 (2019) 837–845], [K.M. Nakprasit and K.
Sribunhung Sarawute +3 more
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