#### Title:

On the Existence of Bipartite Graphs Which are notCyclically-Interval Colorable

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#### Uncontrolled Keywords:

Cyclically interval t-coloring ; bipartite graph

#### Abstract:

A proper edge t-coloring of an undirected, simple, finite, connected graph G is a coloring of its edges with colors 1, 2, ..., t such that all colors are used, and no two adjacent edges receive the same color. A cyclically interval t-coloring of a graph G is a proper edge t-coloring of G such that for each its vertex x, either the set of colors used on edges incident to x or the set of colors not used on edges incident to x forms an interval of integers. For any t ∈ N, let Mt be the set of graphs for which there exists a cyclically-interval t-coloring. Examples of bipartite graphs that do not belong to the class S t≥1 Mt are constructed.

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#### Affiliation:

Institute for Informatics and Automation Problems

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#### Conference title:

11th International Conference on Computer Science and Information Technologies CSIT 2017