A. Tucker, Coloring graphs with stable cutsets, J. Combin. Theory Ser. B 34 (1983) 258--267. Home/Search Document Not in Database Summary Related Articles Check |
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Bisplit Graphs - Brandstädt, Hammer, al. (2002) (Correct)
....this problem is shown in [8] to be NP complete when means the property of being a cograph. Another problem of this type is the stable cutset problem asking whether the input graph G = V; E) has a stable set S such that V nS induces a disconnected graph in G; this problem is NP complete. See [1, 4, 3, 11] for papers discussing the stable cutset problem. Throughout this paper, all graphs are nite, loopless and undirected. For a subset of vertices U of a graph G = V; E) we denote by G[U ] the subgraph of G induced by U . A vertex v 2 V is said to be a neighbor of a vertex u 2 V if it is adjacent ....
A. Tucker, Coloring graphs with stable cutsets, J. Combin. Theory Ser. B 34 (1983) 258-267
The Classes of Critically and Anticritically Perfect Graphs - Wagler (2000) (Correct)
....a graph G if and only if G 2 C or G x 2 C 8x 2 V (G) and G or G has a star cutset, and proved that C is perfect if C is. Thus BIP is a class of perfect graphs where BIP denotes the class of bipartite graphs. Investigating cutsets with pairwise non adjacent nodes, called stable cutsets, Tucker [25] pointed out that the odd holes are the only minimally imperfect graphs containing stable cutsets. We say that x dominates y if N(y) N(x) fxg holds (N(y) contains all nodes adjacent to y) and call x; y a comparable pair which is said to be strict if x; y are non adjacent and weak otherwise. An ....
....of G e . Since G e e must not possess any clique cutset, we have x; y 2 Q. Now, G e e) Q is a star cutset of G e e if it contains more than two nodes, thus (G e e) Q = fx; yg follows due to [5] Therefore, G e e has the stable cutset fx; yg and is, consequently, an odd hole by Tucker [25]. Taking into account that no node in V 0 1 is linked by an edge to any node in V 0 2 , the assertion follows immediately. 2 This lemma provides the opportunity to construct, for each perfect graph F , a critically perfect graph G with F G: Cover all non critical edges of F by cliques Q 1 ; ....
A. Tucker, Coloring Graphs with Stable Cutsets. J. Combin. Theory (B) 34 (1983) 256-267
On Stable Cutsets in Graphs - Brandstädt, Dragan, Le, Szymczak (2000) (8 citations) (Correct)
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A. Tucker, Coloring graphs with stable cutsets, J. Combin. Theory Ser. B 34 (1983) 258--267.
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