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On path-chromatically unique graphs

✍ Scribed by Esperanza Blancaflor Arugay; Severino Villanueva Gervacio

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 230 KB
Volume: 151
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(94)00079-x

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✦ Synopsis

The least number of colors needed to color the vertices of a graph G such that the vertices in each color class induces a linear forest is called the path-chromatic number of G, denoted by Zoo (G).

If all such colorings of the vertices of G induce the same partitioning of the vertices of G, we say that G is path-chromatically unique. We prove here that there exist infinitely many path-chromatically unique graphs with path-chromatic number t, for each t >/1. We also show that pathchromatically unique graphs of order n and path-chromatic number t >i 2 exist only for n 1> 4t -1.

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