EDGE COLORING OF CACTUS GRAPHS WITH GIVEN SPECTRUMS
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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