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Anticritical graphs

Published online by Cambridge University Press:  24 October 2008

Frank Harary  and
Carsten Thomassen
Frank Harary
Affiliation:
University of Michigan
Carsten Thomassen
Affiliation:
Aarhus University
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Abstract

The term ‘critical graph’ has been used most frequently to mean a graph such that the removal of any line decreases the chromatic number. This can be generalized to define a graph G to be ‘critical (μ)’ for an arbitrary invariant, μ if, for each line e, μ(G – e) ≠ μ(G). Analogously we may consider any line e which joins two points not already adjacent in G and define G as ‘anticritical (μ)’ if μ(G + e) ≠ μ(G). Anticritical graphs are investigated here with respect to the following invariants: chromatic number, line-chromatic number, point-connectivity, line-connectivity, point-independence number, line-independence number, diameter, radius, and cyclability number.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 79 , Issue 1 , January 1976 , pp. 11 - 18
Copyright
Copyright © Cambridge Philosophical Society 1976

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References

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