o f (y)+2 } and N G (x) ? O = {o f (x) }) then G is an extended odd hole of type c or d ,
The disjoint union of an odd hole and a singleton is strongly circular-imperfect due to Lemma 11. If G is an extended odd hole, then G is strongly circularimperfect as no extended odd hole is an interlaced odd hole. Let v be a vertex of G. It is straightforward to check that G ? v is bipartite or an interlaced odd hole, and therefore strongly circular-perfect ,
Convex-round graphs are circular-perfect, Journal of Graph Theory, vol.19, issue.3, pp.182-194, 2002. ,
DOI : 10.1002/jgt.10047
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.31.6278
Färbungen von Graphen, deren sämtliche bzw. deren ungerade Kreise starr sind, Wiss, pp.114-115, 1961. ,
A note on the star chromatic number, Journal of Graph Theory, vol.12, issue.4, pp.479-482, 1990. ,
DOI : 10.1002/jgt.3190140412
The strong perfect graph theorem, Annals of Mathematics, vol.164, issue.1 ,
DOI : 10.4007/annals.2006.164.51
Geometric Algorithms and Combinatorial Optimization, 1988. ,
Problems from the world surrounding perfect graphs, Zastos. Mat, vol.19, pp.413-431, 1987. ,
Normal hypergraphs and the weak perfect graph conjecture, Discrete Math, pp.253-267, 1972. ,
Die Bestimmung eines k??rzesten Kreises gerader L??nge, Computing, vol.31, issue.4, pp.31-355, 1983. ,
DOI : 10.1007/BF02251238
Three classes of minimal circular-imperfect graphs, Electronic Notes in Discrete Mathematics, vol.19 ,
DOI : 10.1016/j.endm.2005.05.003
Applying Lehman's theorems to packing problems, Mathematical Programming, vol.13, issue.4, pp.353-367, 1995. ,
DOI : 10.1007/BF01590960
A class of facet producing graphs for vertex packing polyhedra, Discrete Mathematics, vol.12, issue.4, pp.373-388, 1975. ,
DOI : 10.1016/0012-365X(75)90077-1
Star chromatic number, Journal of Graph Theory, vol.20, issue.4, pp.551-559, 1988. ,
DOI : 10.1002/jgt.3190120411
Antiwebs are rank-perfect, Quarterly Journal of the Belgian, French and Italian Operations Research Societies, vol.2, issue.2, pp.149-152, 2004. ,
DOI : 10.1007/s10288-003-0032-4
Circular perfect graphs, Journal of Graph Theory, vol.59, issue.3, pp.186-209, 2005. ,
DOI : 10.1002/jgt.20050
URL : https://hal.archives-ouvertes.fr/hal-00431241