The bipartite vertex (resp. edge) frustration of a graph G, denoted by ψ(G) (resp. φ(G)), is the smallest number of vertices (resp. edges) that have to be deleted from G to obtain a bipartite subgraph of G. A sharp lower bound of the bipartite vertex frustration of the line graph L(G) of every graph G is given. In addition, the exact value of ψ(L(G)) is calculated when G is a forest.

It is well known that imprimitive P -polynomial association schemes X = (X, {Ri}0≤i≤d) with k1 > 2 are either bipartite or antipodal, i.e., intersection numbers satisfy either ai = 0 for all i, or bi = cd−i for all i 6= [d/2]. In this paper, we show that imprimitiveQ-polynomial association schemesX = (X, {Ri}0≤i≤d) with d > 6 and k∗ 1 > 2 are either dual bipartite or dual antipodal, i.e., dual ...

Robertson and Seymour proved that every graph with sufficiently large treewidth contains a large grid minor. However, the best known bound on the treewidth that forces an l × l grid minor is exponential in l. It is unknown whether polynomial treewidth suffices. We prove a result in this direction. A grid-like-minor of order l in a graph G is a set of paths in Gwhose intersection graph is bipart...

The class of Bipartite Distance Hereditary (BDH) graphs is the intersection between bipartite domino-free and chordal bipartite graphs. Graphs in both the latter classes have linearly many maximal bicliques, implying the existence of polynomial-time algorithms for computing the associated Galois lattice. Such a lattice can indeed be built in O(m×n) worst case-time for a domino-free graph with m...

the concept of the bipartite divisor graph for integer subsets has been considered in [‎graph combinator., ‎ 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 $g$ is a solvable group‎, ‎then the number of connected components of this graph is at most $2$ and if $g...

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...

This document presents an overview to the clustComp package, which is a collection of tools developed for the comparison and the visualisation of relationships between two clusterings, either flat versus flat or flat versus hierarchical. Both situations are addressed by representing clusters as nodes in a weighted bipartite graph, where each layer corresponds to one of the clusterings under com...

‎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...