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Critical Graphs for Acyclic Colorings

Published online by Cambridge University Press:  20 November 2018

David M. Berman
David M. Berman*
Affiliation:
Department of Mathematics, University of New Orleans, New Orleans, Louisiana 70122 USA
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The concept of acyclic colorings of graphs, introduced by Grunbaum [2], is a generalization of point-arboricity. An acyclic coloring of a graph is a proper coloring of its points such that there is no two-colored cycle. We denote by a(G), the acyclic chromatic number of a graph G, the minimum number of colors for an acyclic coloring of G. We call G k-critical if a(G) = fc but a(G′) for any proper subgraph G′. For all notation and terminology not defined here, see Harary [3].

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 21 , Issue 1 , 01 March 1978 , pp. 115 - 116
Copyright
Copyright © Canadian Mathematical Society 1978

References

1. B. Bollobás and Harary, F., Point arboricity critical graphs exist, J. London Math. Soc. (2), 12 (1975), 97-102.Google Scholar
2. Griinbaum, B., “Acyclic colorings of planar graphs”, Israel. J. Math., 14 (1973), 390-408.Google Scholar
3. Harary, F., Graph Theory (Addison-Wesley, Reading, Mass., 1969).Google Scholar
4. Kronk, H. V. and Mitchem, J., Critical point-arboritic graphs, J. London Math. Soc. (2), 9 (1975), 459-466.Google Scholar