F-WORM colorings: Results for 2-connected graphs

Csilla Bujtás, Z. Tuza

Research output: Contribution to journalArticle


Given two graphs F and G, an F-WORM coloring of G is an assignment of colors to its vertices in such a way that no F-subgraph of G is monochromatic or rainbow. If G has at least one such coloring, then it is called F-WORM colorable and W(G,F) denotes the minimum possible number of colors. Here, we consider F-WORM colorings with a fixed 2-connected graph F and prove the following three main results: (1) For every natural number k, there exists a graph G which is F-WORM colorable and W(G,F)=k; (2) It is NP-complete to decide whether a graph is F-WORM colorable; (3) For each k≥|V(F)|−1, it is NP-complete to decide whether a graph G satisfies W(G,F)≤k. This remains valid on the class of F-WORM colorable graphs of bounded maximum degree. We also prove that for each n≥3, there exists a graph G and integers r and s such that s≥r+2, G has Kn-WORM colorings with exactly r and also with s colors, but it admits no Kn-WORM colorings with exactly r+1,…,s−1 colors. Moreover, the difference s−r can be arbitrarily large.

Original languageEnglish
Pages (from-to)131-138
Number of pages8
JournalDiscrete Applied Mathematics
Publication statusPublished - Nov 20 2017



  • 2-connected graphs
  • Feasible set
  • Gap in chromatic spectrum
  • Lower chromatic number
  • WORM coloring

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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