Edge coloring signed graphs
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TL;DR: In this paper, the authors define a method for edge coloring signed graphs and what it means for such a coloring to be proper, and show that the minimum number of colors required for a proper coloring of a signed simple graph is bounded above by Δ + 1 in parallel with Vizing's Theorem.
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About: This article is published in Discrete Mathematics. The article was published on 01 Feb 2020. and is currently open access. The article focuses on the topics: Edge coloring & Signed graph.
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Citations
Edge Coloring of the Signed Generalized Petersen Graph
TL;DR: In this paper, the authors considered the edge coloring of signed generalized Petersen graphs and proved that the chromatic index of a signed graph can be computed in the signed version of the signed Vizing Theorem.
1
Vizing's adjacency lemma on edge chromatic critical signed graphs and its applications
TL;DR: In this article , the authors extend Vizing's adjacency lemma to critical signed graphs with even maximum degrees, and show that the signed planar graph conjecture is true for signed graph with maximum degree at least 8.
1
On the Chromatic Index of the Signed Generalized Petersen Graph GP(n, 2)
Shanshan Zheng,Hongyan Cai,Yuanpei Wang,Qiang Sun +3 more
TL;DR: The chromatic index of the signed generalized Petersen graph GP(n,2) was shown to be its maximum degree for most cases in this paper , where the chromatic indices of signed graphs are obtained by a mapping from each vertex-edge incidence of Gσ to a proper q-edge coloring, denoted by χ′(Gσ).
Bounds for the chromatic index of signed multigraphs
Eckhard Steffen,Isaak H. Wolf +1 more
TL;DR: The chromatic index of a signed multigraph with edge-coloring was shown to be at most at most 3/2/3/2 + 1 in this article , where 3 is the number of colors.
Signed planar graphs with Δ ≥ 8 are Δ-edge-colorable
Li Zhang,You Lu,Shenggui Zhang +2 more
TL;DR: In this paper , Zhang et al. proved that every signed planar graph with Δ≥8 is Δ-edge-colorable, where Δ is the maximum degree of the graph.
References
The Chromatic Number of a Signed Graph
TL;DR: A chromatic number for signed graphs was proposed in this paper, which provides a natural extension of the chromatic numbers of an original signed graph to the case of signed planar graphs.
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The chromatic number of a signed graph
TL;DR: The definition of a chromatic number for signed graphs is proposed which provides a natural extension of thechromatic number of an unsigned graph and is establish the basic properties of this invariant.
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Maximum Frustration in Bipartite Signed Graphs
TL;DR: Two results are proved about the maximum frustration of a complete bipartite graph, K_{l,r), with left vertices and right vertices, that is bounded above by there is a unique family of signed $K_{ l,r}$ that reach this bound.
Balanced decompositions of a signed graph
TL;DR: It is proved that, for a complete signed graph, δ1 = δ0; more strongly, with three exceptions a minimal balanced decomposition exists into connected and spanning edge sets.