| Issue |
RAIRO-Theor. Inf. Appl.
Volume 39, Number 1, January-March 2005
Imre Simon, the tropical computer scientist
|
|
|---|---|---|
| Page(s) | 145 - 160 | |
| DOI | https://doi.org/10.1051/ita:2005009 | |
| Published online | 15 March 2005 | |
The perfection and recognition of bull-reducible Berge graphs
1
LORIA, France;
Hazel.Everett@loria.fr
2
Universidade Federal do Rio de Janeiro,
Brasil;
celina@cos.ufrj.br, sula@cos.ufrj.br
3
McGill University,
Canada;
breed@cs.mcgill.ca
The recently announced Strong Perfect Graph Theorem states that the class of perfect graphs coincides with the class of graphs containing no induced odd cycle of length at least 5 or the complement of such a cycle. A graph in this second class is called Berge. A bull is a graph with five vertices x, a, b, c, d and five edges xa, xb, ab, ad, bc. A graph is bull-reducible if no vertex is in two bulls. In this paper we give a simple proof that every bull-reducible Berge graph is perfect. Although this result follows directly from the Strong Perfect Graph Theorem, our proof leads to a recognition algorithm for this new class of perfect graphs whose complexity, O(n6), is much lower than that announced for perfect graphs.
Mathematics Subject Classification: 05C17 / 05C75 / 05C85
© EDP Sciences, 2005
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