Matrices for bipartite graphs and multisets
Skew-adjacency matrices of graphs
... is bipartite but not a forest, it is possible that s n = m n ( G ) for all skew- adjacency matrices of ...Since graphs with no even cycles (the odd-cycle graphs) are in a sense the opposite ...
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Packing bipartite graphs with covers of complete bipartite graphs
... For bipartite graphs, the following are ...in bipartite graphs and showed that the K 2 , 1 -Factor problem stays NP -complete when restricted to the class of bipartite ...for ...
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CiteSeerX — Packing bipartite graphs with covers of complete bipartite graphs
... We now prove that K k, -Pseudo-Cover is NP-complete for all k, ≥ 2. Our proof is inspired by the proof of Hell, Kirkpatrick, Kratochv´ıl, and Kˆr´ıˆ z in [14]. They consider the problem of testing if a graph has an S ...
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Recognizing graphs close to bipartite graphs.
... for graphs of bounded maximum ...near-bipartite graphs is known to be an NP-complete ...for graphs of maximum degree 4 and for graphs of diameter ...for graphs of maximum degree ...
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On the hyperbolicity of bipartite graphs and intersection graphs
... intersection graphs of edges in a graph and have already received some attention in the literature of graph hyperbolicity [8, ...intersection graphs over a ground set S have for vertices a family of subsets ...
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Bipartite Toughness and k Factors in Bipartite Graphs
... Toughness, like connectivity, is an important invariant in graphs. There has been extensive work on toughness see the survey in 1 since Chv´atal introduced the concept in 1973 2. The toughness tG of a graph G is ...
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Planar Graphs, Regular Graphs, Bipartite Graphs and Hamiltonicity
... The advantage of cubic graphs (every vertex of degree 3) when looking for a Hamiltonian cycle is that if two edges incident with a vertex are in a Hamiltonian cycle, then the [r] ...
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Star Coloring of Cartesian Product of Complete Bipartite Graphs, Double Star Graphs with Complete Bipartite Graphs
... In recent decades, G.Fertin et al[2] have given the star coloring of some families of graphs such as trees, cycles, complete bipartite and obtained the bounds for the star chromatic [r] ...
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On the cyclic decomposition of circulant graphs into bipartite graphs
... a bipartite graph G with n edges possesses any of three types of ordered labelings, then the complete graph K 2nx+1 admits a cyclic G-decomposition for every positive integer ...a bipartite graph G admits ...
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On the cyclic decomposition of complete graphs into bipartite graphs
... It has become a tradition for researchers in this area to introduce variations on Rosa's original labelings and to conjecture that all trees have these lahelings.[r] ...
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Bipartite Permutation Graphs are Reconstructible
... Proof of Lemma 3.4. If min{|X|, |Y |} = 1, G is a tree, and is thus reconstructible. Therefore we assume that min{|X|, |Y |} ≥ 2. Let x be a polar vertex adjacent to every vertex in Y . Let L be a permutation diagram ...
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Bipartite Kneser graphs are Hamiltonian
... exceptional graphs (one of the exceptions K(5, 2) we already mentioned), every connected vertex-transitive graph has a Hamilton ...Kneser graphs and bipartite Kneser graphs have this strong ...
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Algorithmic aspects of bipartite graphs
... Algorithms have been developed for computing the fill-in for any ordering of pivots, for generating a perfect ordering if such an ordering exists, and for reducing a fill-in to a minimal[r] ...
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Eigenvalues of Matrices and Graphs
... The structure of the chapter The rest of this chapter is organized as fol- lows. Since our initial motivation was the possible reduction of a large standard eigenproblem to a small polynomial eigenproblem in order to ...
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On graphs with complete bipartite star complements
... Fig. 1. Two maximal graphs. be found using the computer-generated regular subgraphs of Sch 16 identified in [2]. We can however find all the relevant graphs directly in terms of our construction of Sch 10 . ...
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A note on the independence number in bipartite graphs
... vertices of G. For a subset S of V (G), we denote by G[S] the subgraph of G induced by S. A clique is a subset of vertices such that its induced subgraph is complete. The clique number, ω(G), of a graph G is the number ...
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b-coloring of some bipartite graphs ∗
... For notation and graph theory terminology we generally follow [1]. Consider a graph G = (V, E). For any vertex v of G, the neighborhood of v is the set N G (v) = {u ∈ V (G) | (u, v) ∈ E} (or N(v) if there is no ...
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2 Characterization of bipartite graphs with γ
... Theorem 1.1 ([7]) If G is a graph with no isolated vertices, then γ(G) ≤ |G|/2. In 1982, Payan and Xuong, and independently in 1985, Fink, Jacobson, Kinch and Roberts, characterized the graphs achieving equality ...
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Cooperative colorings of trees and of bipartite graphs
... A basic fact about vertex coloring is that every graph G of maximum degree d is (d + 1)-colorable. It is therefore natural to ask whether d + 1 graphs, each of maximum degree d, always have a cooperative coloring. ...
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On the Laplacian spectral radii of bipartite graphs
... Corollary 1.1 [5]. Let G be a graph of order n. Then μ( G ) n, and the equality holds if and only if G is disconnected. There are many literatures on Laplacian spectral radii of some special classes of graphs. ...
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