Results 21 to 30 of about 28,401 (120)
Planar Graphs of Maximum Degree 6 and without Adjacent 8-Cycles Are 6-Edge-Colorable
Journal of Mathematics, 2021 In this paper, by applying the discharging method, we show that if G is a planar graph with a maximum degree of Δ=6 that does not contain any adjacent 8-cycles, then G is of class 1.
Wenwen Zhang
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Precise Upper Bound for the Strong Edge Chromatic Number of Sparse Planar Graphs
Discussiones Mathematicae Graph Theory, 2013 We prove that every planar graph with maximum degree ∆ is strong edge (2∆−1)-colorable if its girth is at least 40+1. The bound 2∆−1 is reached at any graph that has two adjacent vertices of degree ∆.
Borodin Oleg V., Ivanova Anna O.
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The strong chromatic index of 1-planar graphs [PDF]
Discrete Mathematics & Theoretical Computer ScienceThe chromatic index $\chi'(G)$ of a graph $G$ is the smallest $k$ for which $G$ admits an edge $k$-coloring such that any two adjacent edges have distinct colors.
Yiqiao Wang +3 more
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The maximum number of edges of bipartite 1-planar graphs with 1-disk drawings
AKCE International Journal of Graphs and CombinatoricsA graph is 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 bipartition sets X and Y. A 1-disk [Formula: see text] drawing of G is a 1-planar drawing such that all vertices
Guiping Wang
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Discrete Mathematics & Theoretical Computer ScienceNot every directed acyclic graph (DAG) whose underlying undirected graph is planar admits an upward planar drawing. We are interested in pushing the notion of upward drawings beyond planarity by considering upward $k$-planar drawings of DAGs in which the
Patrizio Angelini +10 more
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Neighbor Product Distinguishing Total Colorings of Planar Graphs with Maximum Degree at least Ten
Discussiones Mathematicae Graph Theory, 2021 A proper [k]-total coloring c of a graph G is a proper total coloring c of G using colors of the set [k] = {1, 2, . . . , k}. Let p(u) denote the product of the color on a vertex u and colors on all the edges incident with u.
Dong Aijun, Li Tong
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Negative results on acyclic improper colorings [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 Raspaud and Sopena showed that the oriented chromatic number of a graph with acyclic chromatic number $k$ is at most $k2^{k-1}$. We prove that this bound is tight for $k \geq 3$.
Pascal Ochem
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Structure of Projective Planar Subgraphs of the Graph Obstructions for Fixed Surface
Кібернетика та комп'ютерні технології, 2022 Consider the problem of studying the metric properties of a subgraph G \ v, where v is an arbitrary vertex of obstruction graphs G of a nonorientable genus, which will determine the sets of points of attachment of one subgraph to another and allow ...
Volodymyr Petrenjuk +2 more
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Fast simulation of planar Clifford circuits [PDF]
QuantumA general quantum circuit can be simulated classically in exponential time. If it has a planar layout, then a tensor-network contraction algorithm due to Markov and Shi has a runtime exponential in the square root of its size, or more generally ...
David Gosset +3 more
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Prime labelings on planar grid graphs
Theory and Applications of Graphs, 2022 It is known that for any prime p and any integer n such that 1≤n≤p there exists a prime labeling on the pxn planar grid graph PpxPn.
Stephen James Curran
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