Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-15T19:12:27.520Z Has data issue: false hasContentIssue false

Uniquely Line Colorable Graphs

Published online by Cambridge University Press:  20 November 2018

D. L. Greenwell
Affiliation:
Emory University, Atlanta, Georgia
H. V. Kronk
Affiliation:
Emory University, Atlanta, Georgia
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A line-coloring of a graph G is an assignment of colors to the lines of G so that adjacent lines are colored differently; an n-line coloring uses n colors. The line-chromatic number χ'(G) is the smallest n for which G admits an n-line coloring.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Bosak, J., Hamiltonian lines in cubic graphs, Theory of Graphs (International Symposium, Rome, July 1966), Gordon and Breach, New York, (1967), 3546.Google Scholar
2. Cartwright, D. and Harary, F., On the coloring of signed graphs, Elem. Math. 23 (1968), 8589.Google Scholar
3. Chartrand, G. and Geller, D. P., On uniquely colorable planar graphs, J. Combinatorial Theory, 6 (1969), 271278.Google Scholar
4. Harary, F., Hedetniemi, S. T., and Robinson, R. W., Uniquely Colorable Graphs, J. Combinatorial Theory, 6 (1969), 271278.Google Scholar
5. Harary, F., Errata, J. Combinatorial Theory, 9 (1970), p. 221.Google Scholar
6. Vizing, V. G., A bound on the chromatic class of a p-graph, Diskret Analiz., 3 (1964), 2530.Google Scholar