Interval minors of bipartite graphs were recently introduced by Jacob Fox in the study of Stanley-Wilf limits. We investigate the maximum number of edges in Kr,s-interval minor free bipartite graphs. We determine exact values when r = 2 and describe the extremal graphs. For r = 3, lower and upper bounds are given and the structure of K3,s-interval minor free graphs is studied.

We study the game of Cops and Robbers, where cops try to capture a robber on vertices graph. Meyniel’s conjecture states that for every connected graph G n vertices, cop number is upper bounded by $$O(\sqrt{n})$$ . That is, suffice catch robber. present several families abelian Cayley graphs are Meyniel extremal, i.e., whose This proves bound proved Bradshaw (Discret Math 343:1, 2019) tight. In...

We investigate the supereulerian graph problems within planar graphs, and we prove that if a 2-edge-connected planar graph G is at most three edges short of having two edge-disjoint spanning trees, then G is supereulerian except a few classes of graphs. This is applied to show the existence of spanning Eulerian subgraphs in planar graphs with small edge cut conditions. We also determine several...

For d ≥ 1 and m ≥ 1, a graph has property Pd ,m if there exist at least m vertex-disjoint paths of length at most d between each pair of vertices. Property Pd ,m , which has a strong connection to wide diameter, is one way of measuring the reliability of a network. In this article, we first examine the relationship of Pd ,m to other similar properties and then we prove several results regarding...

We investigate the maximum number of edges in a graph with a prescribed number of 1factors. We also examine the structure of such extremal graphs.

7 n 2  ≤ WW (G1) + WW (G2) + WW (G3) ≤ 2  n + 2 4  + n 2  + 4(n − 1). The corresponding extremal graphs are characterized. Published by Elsevier B.V.