# EDGE COLORING OF CACTUS GRAPHS WITH GIVEN SPECTRUMS

• Albert Khachik Sahakyan Chair of Discrete Mathematics and Theoretical Informatics, Faculty of Informatics and Applied Mathematics, Yerevan State University, Armenia
Keywords: cactus graphs, block-cut tree, edge coloring, restrictions on spectrums, dynamic programming

### Abstract

An edge-coloring of a graph G is a coloring of the graph edges with integers such that the colors of the edges incident to any vertex of G are distinct. For an edge coloring α and a vertex v the set of all the colors of the incident edges of v is called the spectrum of that vertex in α and is denoted by Sa(V). We consider the case where the spectrum for each vertex V is provided S(V), and the problem is to find an edge-coloring α such that for every vertex V, Sa(V) = S(V). We provide an O(N2) algorithm that inds such an edge-coloring for cactus graphs that satisfies all the restrictions. If it is impossible to have an edge-coloring hat satisfiesthe restrictions of the spectrums the algorithm will tell that too.

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Published
2021-06-10
Citations
How to Cite
Albert Khachik Sahakyan. (2021). EDGE COLORING OF CACTUS GRAPHS WITH GIVEN SPECTRUMS. International Academy Journal Web of Scholar, (2(52). https://doi.org/10.31435/rsglobal_wos/30062021/7617
Section
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