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Multicolored Bipartite Ramsey Numbers of Large Cycles
For an integer r ≥ 2 and bipartite graphs H i , where 1≤ i ≤ r the bipartite Ramsey number br ( H 1 , H 2 , …, H r ) is the minimum integer N such that any r -ed...
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Bipartite Decomposition of Graphs Using Chromatic Number
This chapter targets to determine a decomposition of G into bipartite graphs. In a bipartite graph, the vertex set is partitioned into two...
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Star-factorization of the Complete Bipartite Multigraphs
Let λK m,n be a complete bipartite multigraph with two partite sets having m and n vertices, respectively. A K p,q -factorization of λK m,n is a set of K p,q...
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Marchenko–Pastur Law for Spectra of Random Weighted Bipartite Graphs
AbstractWe study the spectra of random weighted bipartite graphs. We establish that, under specific assumptions on the edge probabilities, the...
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Settling the Nonorientable Genus of the Nearly Complete Bipartite Graphs
A graph is said to be nearly complete bipartite if it can be obtained by deleting a set of independent edges from a complete bipartite graph. The...
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Computation of Grundy dominating sequences in (co-)bipartite graphs
A sequence S of vertices of a graph G is called a dominating sequence of G if (1) each vertex v of S dominates a vertex of G that was not dominated...
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Eulerian and Bipartite Binary Delta-matroids
Delta-matroid theory is often thought of as a generalization of topological graph theory. It is well-known that an orientable embedded graph is...
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Panconnectivity in Bipartite Graphs with Large Degree sum
In 1995, Amar et al. introduced the concept of panconnectivity for balanced bipartite graphs, and obtained a degree sum condition. In 2018, Du et...
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Bipartite perfect matching as a real polynomial
We obtain a description of the Bipartite Perfect Matching decision problem as a multilinear polynomial over the Reals. We show that it has full total...
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Coloring Bipartite Graphs with Semi-small List Size
Recently, Alon, Cambie, and Kang introduced asymmetric list coloring of bipartite graphs, where the size of each vertex’s list depends on its part....
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Moore–Penrose Inverse of the Signless Laplacians of Bipartite Graphs
We provide a relation between the Moore–Penrose inverse of the Laplacian and signless Laplacian matrices of a bipartite graph. As a consequence, we...
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On the Set of Stable Matchings in a Bipartite Graph
AbstractThe topic of stable matchings (marriages) in bipartite graphs gained popularity beginning from the appearance of the classical Gale and...
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Bipartite graphs and best proximity pairs
We say that a bipartite graph G ( A , B ) with the fixed parts A and B is proximinal if there is a semimetric space ( X , d ) such that A and B are disjoint...
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The persistence of bipartite ecological communities with Lotka–Volterra dynamics
The assembly and persistence of ecological communities can be understood as the result of the interaction and migration of species. Here we study a...
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Exact SDP relaxations for quadratic programs with bipartite graph structures
For nonconvex quadratically constrained quadratic programs (QCQPs), we first show that, under certain feasibility conditions, the standard...
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Kasteleyn cokernels and perfect matchings on planar bipartite graphs
The determinant method of Kasteleyn gives a method of computing the number of perfect matchings of a planar bipartite graph. In addition, results of...
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Factorisation of the Complete Bipartite Graph into Spanning Semiregular Factors
We enumerate factorisations of the complete bipartite graph into spanning semiregular graphs in several cases, including when the degrees of all the...
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The Rank of the Sandpile Group of Random Directed Bipartite Graphs
We identify the asymptotic distribution of p -rank of the sandpile group of random directed bipartite graphs which are not too imbalanced. We show...
