Abstract
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 language | English |
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Pages (from-to) | 1786-1792 |
Number of pages | 7 |
Journal | Discrete Mathematics |
Volume | 311 |
Issue number | 16 |
DOIs | |
State | Published - 28 Aug 2011 |
Keywords
- Coloring
- Connectivity
- Monochromatic
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics