Article

Combinatorica

, Volume 12, Issue 2, pp 125-134

Colorings and orientations of graphs

  • N. AlonAffiliated withDepartment of Pure Mathematics School of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University
  • , M. TarsiAffiliated withDepartment of Computer Science School of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University

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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: IfG is a directed graph with maximum outdegreed, and if the number of Eulerian subgraphs ofG 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 setS(v) ofd+1 colors for each vertexv ofG there is a legal vertex-coloring ofG assigning to each vertexv a color fromS(v).

AMS Subject Classification codes (1991)

05 C 15 05 C 20