Results 31 to 40 of about 200,785 (277)
Structural properties of 1-planar graphs and an application to acyclic edge coloring [PDF]
, 2010 A graph is called 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. In this paper, we establish a local property of 1-planar graphs which describes the structure in the neighborhood of small vertices (i.e ...
Liu, Guizhen, Wu, Jian-Liang, Zhang, Xin
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Acyclic colouring of 1-planar graphs
Discrete Applied Mathematics, 2001 A graph is said to be 1-planar if it can be embedded into the plane so that each of its edges is crossed by at most one other edge. A coloring of the vertices of a graph is said to be acyclic if every cycle contains at least three colors. The acyclic chromatic number \(a(G)\) of a graph \(G\) is the minimal \(k\) such that \(G\) admits an acyclic \(k\)-
Borodin, O. V. +3 more
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On the Sizes of Bipartite 1-Planar Graphs [PDF]
The Electronic Journal of Combinatorics, 2021 A graph is called $1$-planar if it admits a drawing in the plane such that each edge is crossed at most once. Let $G$ be a bipartite $1$-planar graph with $n$ ($n\ge 4$) vertices and $m$ edges. Karpov showed that $m\le 3n-8$ holds for even $n\ge 8$ and $m\le 3n-9$ holds for odd $n\ge 7$.
Dong, F. M. +2 more
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Strongly Multiplicative Labeling of Diamond Graph, Generalized Petersen Graph, and Some Other Graphs
Journal of Mathematics, 2022 A finite, simple graph of order k is said to be a strongly multiplicative graph when all vertices of the graph are labeled by positive integers 1,2,3,…,k such that the induced edge labels of the graph, obtained by the product of labels of end vertices of
Sumiya Nasir +5 more
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Hosoya Polynomial, Wiener Index, Coloring and Planar of Annihilator Graph of Zn [PDF]
Al-Rafidain Journal of Computer Sciences and Mathematics, 2020 Let R be a commutative ring with identity. We consider ΓB(R) an annihilator graph of the commutative ring R. In this paper, we find Hosoya polynomial, Wiener index, Coloring, and Planar annihilator graph of Zn denote ΓB(Zn) , with n= pm or n=pmq, where p,
Mohammed Ahmed +2 more
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A Sufficient Condition for Planar Graphs of Maximum Degree 6 to be Totally 7-Colorable
Discrete Dynamics in Nature and Society, 2020 A total k-coloring of a graph is an assignment of k colors to its vertices and edges such that no two adjacent or incident elements receive the same color.
Enqiang Zhu, Yongsheng Rao
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Tuza's Conjecture for Threshold Graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2022 Tuza famously conjectured in 1981 that in a graph without k+1 edge-disjoint triangles, it suffices to delete at most 2k edges to obtain a triangle-free graph. The conjecture holds for graphs with small treewidth or small maximum average degree, including
Marthe Bonamy +6 more
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Longer Cycles in Essentially 4-Connected Planar Graphs
Discussiones Mathematicae Graph Theory, 2020 A planar 3-connected graph G is called essentially 4-connected if, for every 3-separator S, at least one of the two components of G − S is an isolated vertex.
Fabrici Igor +3 more
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Planar graphs with $\Delta \geq 7$ and no triangle adjacent to a $C_4$ are minimally edge and total choosable [PDF]
Discrete Mathematics & Theoretical Computer Science, 2016 For planar graphs, we consider the problems of list edge coloring and list total coloring. Edge coloring is the problem of coloring the edges while ensuring that two edges that are adjacent receive different colors.
Marthe Bonamy +2 more
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On Edge Colorings of 1-Planar Graphs without 5-Cycles with Two Chords
Discussiones Mathematicae Graph Theory, 2019 A graph is 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. In this paper, it is proved that every 1-planar graph with maximum degree ∆ ≥ 8 is edge-colorable with ∆ colors if each of its 5-cycles contains ...
Sun Lin, Wu Jianliang
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