Volume 21, No 3, 2014, P. 76-81
À. V. Pyatkin
On edge muticoloring of unicyclic graphs
A muticoloring of an edge weighted graph is an assignment of intervals to its edges such that the intervals of adjacent edges do not intersect in the inner points and the length of each interval is equal to the weight of the edge. The minimum length of the union of all intervals is the edge multichromatic number of the graph. The maximum weighted degree of the vertices (the sum of the weights of the edges incident to it) is its evident lower bound. The examples are known when the multichromatic number is 1.5 times as big as the lower bound. There is a conjecture that this ratio cannot exceed 1.5. In the paper, this conjecture is proved for the class of unicyclic graphs.
Keywords: edge coloring, muticoloring, weighted graphs, intervals, open shop problem.
Pyatkin Artem Valerievich 1,2
1. S. L. Sobolev Institute of Mathematics, SB RAS,
4 Acad. Koptyug Ave., 630090 Novosibirsk, Russia
2. Novosibirsk State University,
2 Pirogov St., 630090 Novosibirsk, Russia