منابع مشابه
Bisimplicial Edges in Bipartite Graphs
Bisimplicial edges in bipartite graphs are closely related to pivots in Gaussian elimination that avoid turning zeroes into non-zeroes. We present a new deterministic algorithm to find such edges in bipartite graphs. The expected time complexity of our new algorithm is O ( n2 log n ) on random bipartite graphs in which each edge is present with a fixed probability p, a polynomial improvement ov...
متن کاملSpanning Cycles Through Specified Edges in Bipartite Graphs
Pósa proved that if G is an n-vertex graph in which any two nonadjacent vertices have degree sum at least n + k, then G has a spanning cycle containing any specified family of disjoint paths with a total of k edges. We consider the analogous problem for a bipartite graph G with n vertices and parts of equal size. Let F be a subgraph of G whose components are nontrivial paths. Let k be the numbe...
متن کاملBisimplicial vertices in even-hole-free graphs
A hole in a graph is an induced subgraph which is a cycle of length at least four. A hole is called even if it has an even number of vertices. An even-hole-free graph is a graph with no even holes. A vertex of a graph is bisimplicial if the set of its neighbours is the union of two cliques. In this paper we prove that every even-hole-free graph has a bisimplicial vertex, which was originally co...
متن کاملChromaticity of Bipartite Graphs with Five or Six Edges Deleted
For integers p, q, s with p ≥ q ≥ 2 and s ≥ 0, let K−s 2 (p, q) denote the set of 2−connected bipartite graphs which can be obtained from Kp,q by deleting a set of s edges. F.M.Dong et al. (Discrete Math. vol.224 (2000) 107–124) proved that for any graph G ∈ K−s 2 (p, q) with p ≥ q ≥ 3 and 0 ≤ s ≤ min{4, q−1}, then G is chromatically unique. In this paper, we shall extend this result to p ≥ q ≥...
متن کاملChromatic Uniqueness of Complete Bipartite Graphs With Certain Edges Deleted
For integers p, q, s with p ≥ q ≥ 2 and s ≥ 0, let K−s 2 (p, q) denote the set of 2−connected bipartite graphs which can be obtained from Kp,q by deleting a set of s edges. In this paper, we prove that for any graph G ∈ K−s 2 (p, q) with p ≥ q ≥ 3, if 11 ≤ s ≤ q − 1 and ∆(G′) = s − 4, where G′ = Kp,q − G, then G is chromatically unique. This result extends both a theorem by Dong et al. [2] and ...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2013
ISSN: 0166-218X
DOI: 10.1016/j.dam.2011.03.004