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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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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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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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Packing four copies of a tree into a complete bipartite graph
In considering packing three copies of a tree into a complete bipartite graph, H. Wang (2009) gives a conjecture: For each tree T of order n and each...
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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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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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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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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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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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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 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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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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Complete Multipartite Graphs Decompositions Using Mutually Orthogonal Graph Squares
Graph theory is a part of mathematics known as combinatorics, and it is one of the most active branches of modern algebra, having numerous...
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Inverse of Hermitian Adjacency Matrix of Mixed Bipartite Graphs
Mixed graph D is a graph that can be obtained from a graph by orienting some of its edges. The Hermitian adjacency matrix of a mixed graph is defined...
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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...
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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...