Colorful monochromatic connectivity

Yair Caro, Raphael Yuster

Research output: Contribution to journalArticlepeer-review


An edge-coloring of a connected graph is monochromatically-connecting if there is a monochromatic path joining any two vertices. How "colorful" can a monochromatically-connecting coloring be? Let mc(G) denote the maximum number of colors used in a monochromatically-connecting coloring of a graph G. We prove some nontrivial upper and lower bounds for mc(G) and relate it to other graph parameters such as the chromatic number, the connectivity, the maximum degree, and the diameter.

Original languageAmerican English
Pages (from-to)1786-1792
Number of pages7
JournalDiscrete Mathematics
Issue number16
StatePublished - 28 Aug 2011


  • Coloring
  • Connectivity
  • Monochromatic

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


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