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864.05034
Hougardy, Stefan; Van Bang Le; Wagler, Annegret
Wing-triangulated graphs are perfect. (English)
[J] J. Graph Theory 24, No.1, 25-31 (1997). [ISSN 0364-9024]
For a graph $G$ the graph $W(G)$ having all edges of $G$ as its vertices, two edges of $G$ being adjacent in $W(G)$ if they are the nonincident edges (called wings) of an induced path on four vertices in $G$, is called the wing-graph of {\it G. C. T. Hoang} [J. Graph Theory 19, No. 2, 271-279 (1995; Zbl 820.05025)] conjectured that if $W(G)$ has no induced cycle of odd length at least five, then $G$ is perfect. In this paper, as a partial result towards Hoang's conjecture, the authors prove that if $W(G)$ is triangulated, then $G$ is perfect.
[ I.Tomescu (Bucuresti) ]
- MSC 1991:
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*05C15 Chromatic theory of graphs and maps
05C38 Paths and cycles
Keywords: perfect graph; triangulated graph; strict quasi-parity graph; wings; induced path; wing-graph
Citations: Zbl 820.05025
Cited in Zbl. reviews...
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