Results 121 to 130 of about 1,017,247 (314)
Bipartite Toughness and k-Factors in Bipartite Graphs
International Journal of Mathematics and Mathematical Sciences, 2008 We define a new invariant tB(G) in bipartite graphs that is analogous to the toughness t(G) and we give sufficient conditions in term of tB(G) for the existence of k-factors in bipartite graphs. We also show that these results are sharp.
Guizhen Liu +3 more
doaj +1 more source
Fractional List Packing for Layered Graphs
Journal of Graph Theory, EarlyView.ABSTRACT The fractional list packing number χ ℓ • ( G ) ${\chi }_{\ell }^{\bullet }(G)$ of a graph G $G$ is a graph invariant that has recently arisen from the study of disjoint list‐colourings. It measures how large the lists of a list‐assignment L : V ( G ) → 2 N $L:V(G)\to {2}^{{\mathbb{N}}}$ need to be to ensure the existence of a “perfectly ...
Stijn Cambie, Wouter Cames van Batenburg
wiley +1 more source
On the deficiency of bipartite graphs
Discrete Applied Mathematics, 1999 An edge-coloring of a graph \(G\) with colors \(1,2,3,\dots\) is consecutive if the set of colors present at each vertex of \(G\) is a consecutive set of integers. For a bipartite graph \(G\), a consecutive edge-coloring has an application in scheduling and thus had been studied before by A. S. Asratian, R. R. Kamalian, D. Hanson, C. O. M.
Krzysztof Giaro +2 more
openaire +1 more source
Bipartite Dot Product Graphs [PDF]
, 2020 Given a bipartite graph G = (X, Y, E), the bipartite dot product representation of G is a function f : X ∪Y → ℝk and a positive threshold t such that for any x ∈ X and y ∈ Y , xy ∈ E if and only if f(x) · f(y) ≥ t. The minimum k such that a bipartite dot
Bailey, Sean, Brown, David E.
core +2 more sources
On Tight Tree‐Complete Hypergraph Ramsey Numbers
Journal of Graph Theory, EarlyView.ABSTRACT Chvátal showed that for any tree T $T$ with k $k$ edges, the Ramsey number R ( T , n ) = k ( n − 1 ) + 1 $R(T,n)=k(n-1)+1$. For r = 3 $r=3$ or 4, we show that, if T $T$ is an r $r$‐uniform nontrivial tight tree, then the hypergraph Ramsey number R ( T , n ) = Θ ( n r − 1 ) $R(T,n)={\rm{\Theta }}({n}^{r-1})$.
Jiaxi Nie
wiley +1 more source
Discrete Mathematics, 2000 The authors study coverings of non-bipartite graphs by bipartite graphs. In particular, they enumerate regular bipartite coverings for orders which are twice a prime.
Archdeacon, D +3 more
openaire +2 more sources
Bipartite matching extendable graphs [PDF]
, 2007 Matching extendability is significant in graph theory and its applications. The basic notion in this direction is n-extendability introduced by Plummer in 1980.
Yixun Lin +5 more
core +1 more source
Lower Bounds for Maximum Weight Bisections of Weighted Triangle‐Free Subcubic Graphs
Journal of Graph Theory, EarlyView.ABSTRACT A bisection of a graph is a cut in which the number of vertices in the two parts of the cut differ by at most 1. In this paper, we consider maximum weight bisections of edge‐weighted triangle‐free subcubic graphs and show that every weighted triangle‐free subcubic graph G = ( V , E , w ) $G=(V,E,w)$ has a bisection with weight at least θ ⋅ w (
Stefanie Gerke +3 more
wiley +1 more source
Bootstrapping Bipartite Graphs Consisting of Edges Based on Ontology Terms Occurring in Scientific Abstract [PDF]
, 2011 The Ontological Discovery Environment (ODE) provides an efficient structure for storage of gene and pheno- type relations. The relations can be represented by a bipartite graph, where the gene and phenotype items can be described as independent sets ...
Morillo, Daniel, Morillo, Daniel.
core
Several results on chordal bipartite graphs [PDF]
, 1997 summary:The question of generalizing results involving chordal graphs to similar concepts for chordal bipartite graphs is addressed. First, it is found that the removal of a bisimplicial edge from a chordal bipartite graph produces a chordal bipartite ...
Bono, Aaron, Bakonyi, Mihály
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