Results 1 to 10 of about 1,282,765 (250)
An improved upper bound for the dynamic list coloring of 1-planar graphs
AIMS Mathematics, 2022 A graph is 1-planar if it can be drawn in the plane such that each of its edges is crossed at most once. A dynamic coloring of a graph G is a proper vertex coloring such that for each vertex of degree at least 2, its neighbors receive at least two ...
Xiaoxue Hu, Jiangxu Kong
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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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A note on nearly Platonic graphs with connectivity one
Electronic Journal of Graph Theory and Applications, 2021 A k-regular planar graph G is nearly Platonic when all faces but one are of the same degree while the remaining face is of a different degree. We show that no such graphs with connectivity one can exist. This complements a recent result by Keith, Froncek,
Dalibor Froncek +3 more
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Computational Study on a PTAS for Planar Dominating Set Problem
Algorithms, 2013 The dominating set problem is a core NP-hard problem in combinatorial optimization and graph theory, and has many important applications. Baker [JACM 41,1994] introduces a k-outer planar graph decomposition-based framework for designing polynomial time ...
Qian-Ping Gu, Marjan Marzban
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SOME PROPERTIES ON COPRIME GRAPH OF GENERALIZED QUATERNION GROUPS
Barekeng, 2023 A coprime graph is a representation of finite groups on graphs by defining the vertex graph as an element in a group and two vertices adjacent to each other's if and only if the order of the two elements is coprime.
Arif Munandar
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Journal of Combinatorial Theory, Series B, 2005 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
McDiarmid, C, Steger, A, Welsh, D
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On certain prime cordial families of graphs
Journal of Taibah University for Science, 2020 Graph labelling is an important tool in modelling real life problems. In the present paper, different graph families are studied for prime cordial labelling.
Nazeran Idrees +3 more
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On Longest Cycles in Essentially 4-Connected Planar Graphs
Discussiones Mathematicae Graph Theory, 2016 A planar 3-connected graph G is essentially 4-connected if, for any 3-separator S of G, one component of the graph obtained from G by removing S is a single vertex.
Fabrici Igor +2 more
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Computing the Girth of a Planar Graph in Linear Time [PDF]
SIAM journal on computing (Print), 2011 The girth of a graph is the minimum weight of all simple cycles of the graph. We study the problem of determining the girth of an n-node unweighted undirected planar graph. The first non-trivial algorithm for the problem, given by Djidjev, runs in O(n5/4
Hsien-Chih Chang, Hsueh-I Lu
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Sufficient Conditions of 6-Cycles Make Planar Graphs DP-4-Colorable
Mathematics, 2022 In simple graphs, DP-coloring is a generalization of list coloring and thus many results of DP-coloring generalize those of list coloring. Xu and Wu proved that every planar graph without 5-cycles adjacent simultaneously to 3-cycles and 4-cycles is 4 ...
Kittikorn Nakprasit +2 more
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