Results 21 to 30 of about 934,158 (291)
Properly Edge-colored Theta Graphs in Edge-colored Complete Graphs [PDF]
Graphs and Combinatorics, 2018 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ruonan Li, Hajo Broersma, Shenggui Zhang
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A note on edge colorings and trees
Mathematical Logic Quarterly, 2022 AbstractWe point out some connections between existence of homogenous sets for certain edge colorings and existence of branches in certain trees. As a consequence, we get that any locally additive coloring (a notion introduced in the paper) of a cardinal κ has a homogeneous set of size κ provided that the number of colors μ satisfies .
Adi Jarden, Ziv Shami
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On star and biclique edge‐colorings [PDF]
International Transactions in Operational Research, 2016 AbstractA biclique of G is a maximal set of vertices that induces a complete bipartite subgraph of G with at least one edge, and a star of a graph G is a maximal set of vertices that induces a complete bipartite graph . A biclique (resp. star) edge‐coloring is a coloring of the edges of a graph with no monochromatic bicliques (resp. stars).
Simone Dantas +5 more
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Discrete Mathematics, 1996 The authors investigate the largest fraction of edges in a 3-regular graph that can be colored in 3 colors. They show that this fraction is always at least 13/15 and sometimes at most 25/27. They investigate the analogous problem for graphs of maximum degree 3 and also for 4-regular graphs with 4 colors instead of 3.
Michael O. Albertson, Ruth Haas
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Degenerate matchings and edge colorings [PDF]
Discrete Applied Mathematics, 2018 A matching $M$ in a graph $G$ is $r$-degenerate if the subgraph of $G$ induced by the set of vertices incident with an edge in $M$ is $r$-degenerate. Goddard, Hedetniemi, Hedetniemi, and Laskar (Generalized subgraph-restricted matchings in graphs, Discrete Mathematics 293 (2005) 129-138) introduced the notion of acyclic matchings, which coincide with ...
Baste, Julien, Rautenbach, Dieter
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Journal of Combinatorial Theory, Series B, 2004 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Paul N. Balister +3 more
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Edge-Coloring Bipartite Graphs [PDF]
Journal of Algorithms, 2000 This note provides an algorithm for finding \(\Delta\)(colors)-edge-coloring of a bipartite graph of order \(n\) and size \(m\) in time \(T+O(m\log \Delta)\) where \(T\) is the time needed to find a perfect matching in a \(k\)-regular bipartite graph, \(k\leq \Delta\), and \(\Delta\) is the maximum degree of vertices.
Ajai Kapoor, Romeo Rizzi
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Facial graceful coloring of plane graphs [PDF]
Opuscula MathematicaLet \(G\) be a plane graph. Two edges of \(G\) are facially adjacent if they are consecutive on the boundary walk of a face of \(G\). A facial edge coloring of \(G\) is an edge coloring such that any two facially adjacent edges receive different colors ...
Július Czap
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Electronic Notes in Discrete Mathematics, 2008 Abstract A split graph is a graph whose vertex set admits a partition into a stable set and a clique. The chromatic indexes for some subsets of split graphs, such as split graphs with odd maximum degree and split-indifference graphs, are known. However, for the general class, the problem remains unsolved.
S. M. ALMEIDA +2 more
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Improved Bounds for Some Facially Constrained Colorings
Discussiones Mathematicae Graph Theory, 2023 A facial-parity edge-coloring of a 2-edge-connected plane graph is a facially-proper edge-coloring in which every face is incident with zero or an odd number of edges of each color. A facial-parity vertex-coloring of a 2-connected plane graph is a proper
Štorgel Kenny
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