The bipartite Star123-free graphs were introduced by V. Lozin in [1] to generalize some already known classes of bipartite graphs. In this paper, we extend to bipartite Star123-free graphs a linear time algorithm of J. L. Fouquet, V. Giakoumakis and J. M. Vanherpe for finding a maximum matching in bipartite Star123, P7-free graphs presented in [2]. Our algorithm is a solution of Lozin’s conject...

Mrvar and Doreian recently defined a notion of bipartite clustering in bipartite signed graphs that gives a measure of imbalance of the signed graph, different from previous measures (the “frustration index” or “line index of balance”, l, and Davis’s clusterability). A biclustering of a bipartite signed graph is a pair (π1, π2) of partitions of the two color classes; the sets of the partitions ...

The Turán number ex(n,H) of a graph H is the maximum number of edges in a graph of order n not containing a copy of H. Given a bipartite graph H and an edge uv in H, let L be obtained from H by adding a path of odd length l ≥ 3 between u and v via l − 1 new vertices. We prove that ex(n,L) ≤ 2ex(n,H)) +O(n3/2). Hence, if ex(n,H) = O(nα) for some α ≥ 3 2 , then ex(n,L) = O(n α) as well. Let L den...

We call a bipartite graph homogeneous if every finite partial automorphism which respects left and right can be extended to a total automorphism. A (κ, λ) bipartite graph is a bipartite graph with left side of size κ and right side of size λ. We show that there is a homogeneous (א0, 2א0) bipartite graph of girth 4 (thus answering negatively a question by Kupitz and Perles), and that depending o...

‎in this paper we give a characterization of unmixed tripartite‎ ‎graphs under certain conditions which is a generalization of a‎ ‎result of villarreal on bipartite graphs‎. ‎for bipartite graphs two‎ ‎different characterizations were given by ravindra and villarreal‎. ‎we show that these two characterizations imply each other‎.

It is a classical result from graph theory that the edges of an l{regular bipartite graph can be colored using exactly l colors so that edges that share an endpoint are assigned diierent colors. In this paper we study two constrained versions of the bipartite edge coloring problem. { Some of the edges adjacent to a pair of opposite vertices of an l-regular bipartite graph are already colored wi...

1 Online bipartite matching Recall from last time we introduced the online bipartite matching problem and gave an algorithm to solve a fractional version of the problem with competitive ratio 1− 1/e. In the online bipartite matching problem, we are given a bipartite graph G = (L,R,E), where the vertices in R are revealed to us one at a time along with the edges from that vertex to L. Once each ...

Given an undirected graph G, an L(h, k)-labelling of G assigns colors to vertices from the integer set {0, . . . , λh,k}, such that any two vertices vi and vj receive colors c(vi) and c(vj) satisfying the following conditions: i) if vi and vj are adjacent then |c(vi)− c(vj)| ≥ h; ii) if vi and vj are at distance two then |c(vi)− c(vj)| ≥ k. The aim of the L(h, k)-labelling problem is to minimiz...

‎In this paper we give a characterization of unmixed tripartite‎ ‎graphs under certain conditions which is a generalization of a‎ ‎result of Villarreal on bipartite graphs‎. ‎For bipartite graphs two‎ ‎different characterizations were given by Ravindra and Villarreal‎. ‎We show that these two characterizations imply each other‎.

‎the concept of the bipartite divisor graph for integer subsets has been considered in [‎m‎. ‎a‎. ‎iranmanesh and c‎. ‎e‎. ‎praeger‎, ‎bipartite divisor graphs for integer subsets‎, ‎{em graphs combin.}‎, ‎{bf 26} (2010) 95--105‎.]‎. ‎in this paper‎, ‎we will consider this graph for the set of character degrees of a finite group $g$ and obtain some properties of this graph‎. ‎we show that if $g...