Geodesic
The perfection and recognition of bull-reducible Berge graphs
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 39 (2005) no. 1, pp. 145-160

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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(n 6 ), is much lower than that announced for perfect graphs.

DOI : 10.1051/ita:2005009
Classification : 05C17, 05C75, 05C85

Everett, Hazel  ; de Figueiredo, Celina M. H.  ; Klein, Sulamita  ; Reed, Bruce 1

1 McGill University, Canada; 
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     title = {The perfection and recognition of bull-reducible {Berge} graphs},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
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Everett, Hazel; de Figueiredo, Celina M. H.; Klein, Sulamita; Reed, Bruce. The perfection and recognition of bull-reducible Berge graphs. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 39 (2005) no. 1, pp. 145-160. doi: 10.1051/ita:2005009

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