Co-author(s) :

Casselgren Carl Johan ; Petrosyan Petros

Abstract:

A proper edge coloring of a graph G with colors 1,2.....,t is called a cyclic interval t coloring if for each vertex v of G the edges incident to v are colored by consecutive colors, under the condition that color 1 is considered as consecutive to color t. We prove that a bipartite graph G of even maximum degree ^ (G) ≥ 4 admits a cyclic interval ^ (G)-coloring if for every vertex v the degree dG (ν) satisfies either dG(ν) ≥ ^(G) -2 or dG(ν) < 2. We also prove that every Eulerian bipartite graph G with maximum degree at most eight has a cyclic interval coloring. Some results are obtained for (a, b)-biregular graphs, that is, bipartite graphs with the vertices in one part all having degree a and the vertices in the other part all having degree b ; it has been conjectured that all these have cyclic interval colorings. We show that all (4,7)-biregular graphs as well as all (2r - 2,2r)-biregular (r ≥2) graphs have cyclic interval colorings. Finally, we prove that all complete multipartite graphs admit cyclic interval colorings; this proves a conjecture of Petrosyan and Mkhitaryan.

Date of publication:

30.05.2017

Identifier:

oai:noad.sci.am:136104

DOI:

10.1002/jgt.22154

ISSN:

0364-9024

Language:

English

Journal or Publication Title:

Graph Theory

Volume:

87

Number:

2

URL:

click here to follow the link

Additional Information:

carl.johan.casselgren@liu.se

Affiliation:

Linköping University ; Department of Mathematics ; Yerevan State University ; Department of Informatics and Applied Mathematics

Country:

Armenia ; Sweden

Indexing:

WOS