Pk -factorization of a complete bipartite graph for k, an even integer was studied by H. Wang [1]. Further, Beiling Du [2] extended the work of H.Wang, and studied the P2k-factorization of complete bipartite multigraph. For odd value of k the work on factorization was done by a number of researchers[3,4,5]. P3-factorization of complete bipartite graph was studied by K.Ushio [3]. P5-factorizatio...

Let Fq be a finite field, where q = p for some odd prime p and integer e ≥ 1. Let f, g ∈ Fq[x, y] be monomials. The monomial graph Gq(f, g) is a bipartite graph with vertex partition P ∪L, P = Fq = L, and (x1, x2, x3) ∈ P is adjacent to [y1, y2, y3] ∈ L if and only if x2 + y2 = f(x1, y1) and x3 + y3 = g(x1, y1). Dmytrenko, Lazebnik, and Williford proved in [6] that if p ≥ 5 and e = 23 for integ...

|This paper describes an algorithm for nding all the perfect matchings in a bipartite graph. By using the binary partitioning method, our algorithm requires O(c(n+m) + n 2:5 ) computational e ort and O(nm) memory storage, (where n denotes the number of vertices, m denotes the number of edges, and c denotes the number of perfect matchings in the given bipartite graph). Keywords|bipartite graph, ...

For a nontrivial connected graph G, non-empty set S \(\subseteq\) V (G) is bipartite dominating of if the subgraph G[S] induced by and for every vertex not in dominated any S. The domination number denoted \(\gamma\)bip(G) G minimum cardinality G. In this paper, we determine exact crown its mycielski as well path cycle graphs.

We give an algorithmic computation for the height of Kauffman’s clock lattice obtained from a knot diagram with two adjacent regions starred and without crossing information specified. We show that this lattice is more familiarly the graph of perfect matchings of a bipartite graph obtained from the knot diagram by overlaying the two dual Tait graphs of the knot diagram. Furthermore we prove str...

A graph is d-bounded if its maximum degree is at most d. We apply the Ore– Ryser Theorem on f -factors in bipartite graphs to obtain conditions for the extension of a 2-bounded subgraph to a 2-factor in a bipartite graph. As consequences, we prove that every matching in the 5-dimensional hypercube extends to a 2-factor, and we obtain conditions for this property in general regular bipartite gra...

A minimal blocker in a bipartite graph G is a minimal set of edges the removal of which leaves no perfect matching in G. We give an explicit characterization of the minimal blockers of a bipartite graph G. This result allows us to obtain a polynomial delay algorithm for finding all minimal blockers of a given bipartite graph. Equivalently, this gives a polynomial delay algorithm for listing the...

The boxicity of a graph G is defined as the minimum integer k such that G is an intersection graph of axis-parallel k-dimensional boxes. Chordal bipartite graphs are bipartite graphs that do not contain an induced cycle of length greater than 4. It was conjectured by Otachi, Okamoto and Yamazaki that chordal bipartite graphs have boxicity at most 2. We disprove this conjecture by exhibiting an ...

The Ramsey number R(m,n) is the smallest integer p such that any blue-red colouring of the edges of the complete graph Kp forces the appearance of a blue Km or a red Kn. Bipartite Ramsey problems deal with the same questions but the graph explored is the complete bipartite graph instead of the complete graph. We investigate the appearance of simpler monochromatic graphs such as stripes, stars a...