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 and five edges . 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, , is much lower than that announced for perfect graphs.
Everett, Hazel ; de Figueiredo, Celina M. H. ; Klein, Sulamita ; Reed, Bruce 1
@article{ITA_2005__39_1_145_0,
author = {Everett, Hazel and de Figueiredo, Celina M. H. and Klein, Sulamita and Reed, Bruce},
title = {The perfection and recognition of bull-reducible {Berge} graphs},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
pages = {145--160},
year = {2005},
publisher = {EDP Sciences},
volume = {39},
number = {1},
doi = {10.1051/ita:2005009},
mrnumber = {2132584},
zbl = {1063.05055},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ita:2005009/}
}
TY - JOUR AU - Everett, Hazel AU - de Figueiredo, Celina M. H. AU - Klein, Sulamita AU - Reed, Bruce TI - The perfection and recognition of bull-reducible Berge graphs JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2005 SP - 145 EP - 160 VL - 39 IS - 1 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/ita:2005009/ DO - 10.1051/ita:2005009 LA - en ID - ITA_2005__39_1_145_0 ER -
%0 Journal Article %A Everett, Hazel %A de Figueiredo, Celina M. H. %A Klein, Sulamita %A Reed, Bruce %T The perfection and recognition of bull-reducible Berge graphs %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2005 %P 145-160 %V 39 %N 1 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/ita:2005009/ %R 10.1051/ita:2005009 %G en %F ITA_2005__39_1_145_0
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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