Rainbow induced subgraphs in proper vertex colorings

Andrzej Kisielewicz; Marek Szykuła

Rainbow induced subgraphs in proper vertex colorings

Combinatorics 2011-05-19 v1

Authors: Andrzej Kisielewicz , Marek Szykuła

Abstract

For a given graph $H$ we define $\rho(H)$ to be the minimum order of a graph $G$ such that every proper vertex coloring of $G$ contains a rainbow induced subgraph isomorphic to $H$ . We give upper and lower bounds for $\rho(H)$ , compute the exact value for some classes of graphs, and consider an interesting combinatorial problem connected with computation of $\rho(H)$ for paths. This research is motivated by some ideas in on-line graph coloring algorithms.

Keywords

rainbow induced subgraph proper vertex coloring graph order extremal graph theory on-line coloring combinatorial bounds

Cite

@article{arxiv.1105.3712,
  title  = {Rainbow induced subgraphs in proper vertex colorings},
  author = {Andrzej Kisielewicz and Marek Szykuła},
  journal= {arXiv preprint arXiv:1105.3712},
  year   = {2011}
}

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