论文信息 - Decomposition of odd-hole-free graphs by double star cutsets and 2-joins

Decomposition of odd-hole-free graphs by double star cutsets and 2-joins

In this paper we decompose odd-hole-free graphs (graphs that do not contain as an induced subgraph a chordless cycle of odd length greater than three) with double star cutsets and 2-joins into bipartite graphs, line graphs of bipartite graphs and the complements of line graphs of bipartite graphs.

[1] Klaus Truemper,et al. Alpha-balanced graphs and matrices and GF(3)-representability of matroids , 1982, J. Comb. Theory, Ser. B.

[2] Gérard Cornuéjols,et al. Even-hole-free graphs part I: Decomposition theorem , 2002 .

[3] Gérard Cornuéjols,et al. Square-free perfect graphs , 2004, J. Comb. Theory, Ser. B.

[4] Gérard Cornuéjols,et al. Even‐hole‐free graphs part II: Recognition algorithm , 2002, J. Graph Theory.

[5] Gérard Cornuéjols,et al. Perfect Graphs, Partitionable Graphs and Cutsets , 2002, Comb..

[6] Gérard Cornuéjols,et al. Even‐hole‐free graphs part I: Decomposition theorem , 2002, J. Graph Theory.

[7] Gérard Cornuéjols,et al. A Mickey-Mouse Decomposition Theorem , 1995, IPCO.

[8] Gérard Cornuéjols,et al. Compositions for perfect graphs , 1985, Discret. Math..

[9] Vasek Chvátal,et al. Star-cutsets and perfect graphs , 1985, J. Comb. Theory, Ser. B.

[10] Gérard Cornuéjols,et al. Graphs without odd holes, parachutes or proper wheels: a generalization of Meyniel graphs and of line graphs of bipartite graphs , 2003, J. Comb. Theory, Ser. B.

[11] Gérard Cornuéjols,et al. Even‐hole‐free graphs part II: Recognition algorithm , 2002, J. Graph Theory.

[12] P. Seymour,et al. The Strong Perfect Graph Theorem , 2002, math/0212070.