TY - GEN
A1 - Asratian Armen
A2 - Casselgren Carl J.
A2 - Petrosyan Petros
N2 - A proper edge-coloring of a graph G with colors 1, . . . , t is called an interval (interval cyclic) t-coloring if all colors are used, and the edges incident to each vertex v 2 V (G) are colored by dG(v) consecutive colors (modulo t), where dG(v) is the degree of a vertex v in G. A graph G is interval (interval cyclically) colorable if it has an interval (interval cyclic) t-coloring for some positive integer t. An (a, b)-biregular bipartite graph G is a bipartite graph G with the vertices in one part all having degree a and the vertices in the other part all having degree b. In 1995, Toft conjectured that all biregular bipartite graphs are interval colorable. This conjecture remains open even for (4, 3)-biregular bipartite graphs. Recently, Casselgren and Toft suggested the following weaker version of the Toftâ€™s conjecture: all biregular bipartite graphs are interval cyclically colorable. They also proved this conjecture for all (8, 4)- biregular bipartite graphs. In this paper we prove the last conjecture for all (a, b)-biregular bipartite graphs when (a, b) 2 {(5, 3), (6, 4), (7, 4), (8, 6)}.
L1 - http://noad.sci.am/Content/135973/DMCA3.pdf
L2 - http://noad.sci.am/Content/135973
T1 - On Interval Cyclic Colorings of Bipartite Graphs
UR - http://noad.sci.am/dlibra/docmetadata?id=135973
ER -