Abstract
Bounds for the chromatic number and for some related parameters of a graph are obtained by applying algebraic techniques. In particular, the following result is proved: If G is a directed graph with maximum outdegree d, and if the number of Eulerian subgraphs of G with an even number of edges differs from the number of Eulerian subgraphs with an odd number of edges then for any assignment of a set S(v) of d+1 colors for each vertex v of G there is a legal vertex-coloring of G assigning to each vertex v a color from S(v).
Original language | English |
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Pages (from-to) | 125-134 |
Number of pages | 10 |
Journal | Combinatorica |
Volume | 12 |
Issue number | 2 |
DOIs | |
State | Published - Jun 1992 |
Keywords
- AMS Subject Classification codes (1991): 05C15, 05C20