A graph is well-covered if every maximal independent set is maximum. This concept, introduced by Plummer in 1970 (J. Combin. Theory 8 (1970)), is the focal point of much interest and current research. We consider well-covered 2-degenerate graphs and supply a structural (and polynomial time algorithm
Packing and covering dense graphs
โ Scribed by Noga Alon; Yair Caro; Raphael Yuster
- Publisher
- John Wiley and Sons
- Year
- 1998
- Tongue
- English
- Weight
- 498 KB
- Volume
- 6
- Category
- Article
- ISSN
- 1063-8539
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๐ SIMILAR VOLUMES
A graph G is called well covered if every two maximal independent sets of G have the same number of vertices. In this paper, we,characterize well covered simplicial, chordal and circular arc graphs.
For two integers a and b, we say that a bipartite graph G admits an (a, b)bipartition if G has a bipartition (X, Y ) such that |X| = a and |Y | = b. We say that two bipartite graphs G and H are compatible if, for some integers a and b, both G and H admit (a, b)-bipartitions. In this paper, we prove
In this article, we study cycle coverings and 2-factors of a claw-free graph and those of its closure, which has been defined by the first author (On a closure concept in claw-free graphs, J Combin Theory Ser B 70 (1997), 217-224). For a claw-free graph G and its closure cl(G), we prove: ( 1 (2) G
For a graph G, let ฯ 3 (G) = min{deg G x + deg G y + deg G z: {x, y, z} is an independent set in G}. Enomoto et al. [Enowoto et al., J Graph Theory 20 (1995), 419-422] have proved that the vertex set of a 2-connected graph G of order n with ฯ 3 (G) โฅ n is covered by two cycles, edges or vertices. Ex