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Chromatically Supremal Decompositions of Graphs

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Abstract

If G is a graph, a G-decomposition of a host graph H is a partition of the edges of H into subgraphs of H which are isomorphic to G. The chromatic index of a G-decomposition of H is the minimum number of colors required to color the parts of the decomposition so that parts which share a common node get different colors. We establish an upper bound on the chromatic index and characterize those decompositions which achieve it. The structurally most interesting of the decompositions with maximal chromatic index are associated with (v, k, 1)-designs.

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Authors and Affiliations

  1. Discrete Mathematics, Clemson University, Clemson, SC, 29634-0975, USA

    Robert E. Jamison

  2. University of Haifa, Haifa, Israel

    Robert E. Jamison

  3. Department of Mathematics, University of Toronto, Toronto, ON, M5S 3G3, Canada

    Eric Mendelsohn

Authors
  1. Robert E. Jamison
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  2. Eric Mendelsohn
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Correspondence to Robert E. Jamison.

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Jamison, R.E., Mendelsohn, E. Chromatically Supremal Decompositions of Graphs. Graphs and Combinatorics 26, 369–382 (2010). https://doi.org/10.1007/s00373-010-0876-2

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  • DOI: https://doi.org/10.1007/s00373-010-0876-2

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