On sum edge-coloring of regular, bipartite and split graphs

An edge-coloring of a graph G with natural numbers is called a sum edge-coloring if the colors of edges incident to any vertex of G are distinct and the sum of the colors of the edges of G is minimum. The edge-chromatic sum of a graph G is the sum of the colors of edges in a sum edge-coloring of G....

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Bibliographic Details
Published inDiscrete Applied Mathematics Vol. 165; pp. 263 - 269
Main Authors Petrosyan, P.A., Kamalian, R.R.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 11.03.2014
Subjects
Algorithms
Bipartite graph
Edge-coloring
Graphs
Mathematical analysis
Polynomials
Regular graph
Split graph
Sum edge-coloring
Upper bounds
Edge-coloring
Split graph
Sum edge-coloring
Bipartite graph
Regular graph
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Summary:An edge-coloring of a graph G with natural numbers is called a sum edge-coloring if the colors of edges incident to any vertex of G are distinct and the sum of the colors of the edges of G is minimum. The edge-chromatic sum of a graph G is the sum of the colors of edges in a sum edge-coloring of G. It is known that the problem of finding the edge-chromatic sum of an r-regular (r≥3) graph is NP-complete. In this paper we give a polynomial time (1+2r(r+1)2)-approximation algorithm for the edge-chromatic sum problem on r-regular graphs for r≥3. Also, it is known that the problem of finding the edge-chromatic sum of bipartite graphs with maximum degree 3 is NP-complete. We show that the problem remains NP-complete even for some restricted class of bipartite graphs with maximum degree 3. Finally, we give upper bounds for the edge-chromatic sum of some split graphs.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2013.09.025