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Graphs without odd holes, parachutes or proper wheels: a generalization of Meyniel graphs and of line graphs of bipartite graphs

Michele Conforti, Gérard Cornuéjols
2003 Journal of combinatorial theory. Series B (Print)  
This is done by showing the following theorem: If a graph G contains no odd hole, no parachute and no proper wheel, then G is bipartite or the line graph of a bipartite graph or G contains a star cutset  ...  The first is a generalization of the Burlet-Fonlupt decomposition of Meyniel graphs by clique cutsets and amalgams.  ...  The class of WP-free graphs containing no odd hole includes the class of Meyniel graphs and the class of line graphs of bipartite graphs.  ... 
doi:10.1016/s0095-8956(02)00021-7 fatcat:r4xn3mvb3rbabfvtyf4ip3l7fu

Page 8953 of Mathematical Reviews Vol. , Issue 2003m [page]

2003 Mathematical Reviews  
8953 Graph theory 2003m:05174 05C75 05C17 Conforti, Michele (I-PADV-PM; Padua); Cornuéjols, Gérard (1-CMU-I; Pittsburgh, PA) Graphs without odd holes, parachutes or proper wheels: a generalization of Meyniel  ...  This is done by showing the following theorem: “Ifa graph G contains no odd hole, no parachute and no proper wheel, then G is bipartite or the line graph of a bipartite graph or G contains a star cutset  ... 

Page 159 of Mathematical Reviews Vol. , Issue Index [page]

Mathematical Reviews  
(English summary) 2003¢:05189 — (with Cornuéjols, Gérard) Graphs without odd holes, parachutes or proper wheels: a generalization of Meyniel graphs and of line graphs of bipartite graphs.  ...  Origins and genesis. 2003e:05055 Boros, Endre (with Gurvich, V. A.; Hougardy, Stefan) Recursive generation of partition- able graphs.  ...