In this paper, we introduce edge coloring for signed graphs which is naturally corresponding to the vertex coloring of their signed line graphs. Let chi(+/-)'(G, sigma) denote the edge chromatic number of a signed graph (G, sigma). It follows from the definition that chi(+/-)'(G, ...
It is well-known that switching equivalence is an equivalence relation in the set of all signed graphs with a fixed underlying graph. In 2020, Behr [2] introduced a concept of edge coloring of signed graphs as a generalization of ordinary graph edge coloring. Let n be a positive integer ...
Line-coloring of signed graphs TY - JOURAU - Chartrand, G.AU - Behzad, M.TI - Line-Coloring of Signed Graphs.JO - Elemente der MathematikPY - 1969VL - 24SP - 49EP - 52LA - engKW - graph theory; line coloring; signed graph;UR - http://eudml.org/doc/140926ER - M Behzad,G...
Edge coloring signed graphsdoi:10.1016/J.DISC.2019.111654Richard BehrNorth-Holland
Signed graphHomomorphismMinorEdge-coloringA signed graph (G, Sigma) is a graph G and a subset Sigma of its edges which corresponds to an assignment of signs to the edges: edges in Sigma are negative while edges not in Sigma are positive. A closed walk of a signed graph is balanced if ...
The paper is devoted to a Gram classification of an important class of signed graphs with loops playing an important role in many branches of mathematics, physics and computer science including game theory, crystallography, Diophantine geometry, Lie theory, spectral graph theory, a graph coloring ...
We study homomorphism problems of signed graphs from a computational point of view. A signed graph (G,Σ) is a graph G where each edge is given a sign, positive or negative; Σ⊆E(G) denotes the set of negative edges. Thus, (G,Σ) is a 2-edge-coloured graph with the property ...
Smallest not C2l+1-colorable graphs of odd-girth 2k+1 manuscript http://arxiv.org/abs/1610.03685 (2016) Google Scholar [3] M. Chudnovsky, K. Edwards, K. Kawarabayashi, P.D. Seymour Edge-coloring seven-regular planar graphs J. Combin. Theory Ser. B, 115 (2015), pp. 276-302 View...
We define a method for edge coloring signed graphs and what it means for such a coloring to be proper. Our method has many desirable properties: it specializes to the usual notion of edge coloring when the signed graph is all-negative, it has a natural definition in terms of vertex ...
These concepts were motivated from a study on balanced signed graphs.doi:10.1016/0095-8956(83)90081-3B. Devadas AcharyaElsevier Inc.Journal of Combinatorial Theory, Series BB.Devadas Acharya.Even Edge Colorings of a Graph[].Journal of Combinatorial Theoryseries B.1983...