The concept of X-chromatic partition and hyper independent chromatic partition of bipartite graphs were introduced by Stephen Hedetniemi and Renu Laskar. We find the bounds for X-chromatic number and hyper independent chromatic number of a bipartite graph. The existence of bipartite graph with χh(G)=a and γY(G)=b-1, χh(G)=a and χX(G)=b where a ≤b are proved. We also prove the existence of bipar...

We show that a minimum edge-colouring of a bipartite graph can be found in O((m) time, where and m denote the maximum degree and the number of edges of G, respectively. It is equivalent to nding a perfect matching in a k-regular bipartite graph in O(km) time. By sharpening the methods, a minimum edge-colouring of a bipartite graph can be found in O((p max (() + log)m) time, where p max (() is t...

Label propagation (LP) is a popular graph-based semi-supervised learning framework. Its effectiveness limited by the distribution of prior labels. If there are no objects with labels in parts classes, label has very poor performance. To address this issue, we propose based on bipartite graph (LPBBG) algorithm. This approach try to learn as exemplar constraints that reflect relations between and...

R. Häggkvist proved that every 3-regular bipartite graph of order 2n with no component isomorphic to the Heawood graph decomposes the complete bipartite graph K6n,6n. In [1] Cichacz and Froncek established a necessary and sufficient condition for the existence of a factorization of the complete bipartite graph Kn,n into generalized prisms of order 2n. In [2] and [3] Cichacz, Froncek, and Kovar ...

In this paper, we study (1, 2)-step competition graphs of bipartite tournaments. A bipartite tournament means an orientation of a complete bipartite graph. We show that the (1, 2)-step competition graph of a bipartite tournament has at most one non-trivial component or consists of exactly two complete components of size at least three and, especially in the former, the diameter of the nontrivia...

Chordal bipartite graph are exactly those bipartite graph in which every cycle of length at least six has a chord. The treewidth of a graph G is the smallest maximum cliquesize among all chordal supergraphs of G decreased by one. We present a polynomial time algorithm for the exact computation of the treewidth of all chordal bipartite graphs. keywords: Graph algorithms, Algorithms and Data Stru...

There has been recent work done in the area of search result organization for image retrieval. The main aim is to cluster the search results into semantically meaningful groups. A number of works benefited from the use of the bipartite spectral graph partitioning method [3][4]. However, the previous works mentioned use a set of keywords for each corresponding image. This will cause the bipartit...