We study a problem on edge percolation on product graphs G× K2. Here G is any finite graph and K2 consists of two vertices {0, 1} connected by an edge. Every edge in G × K2 is p...
Given a non-planar graph G with a subdivision of K5 as a subgraph, we can either transform the K5-subdivision into a K3,3-subdivision if it is possible, or else we obtain a partit...
For all integers k 3, we give an O(n4 ) time algorithm for the problem whose instance is a graph G of girth at least k together with k vertices and whose question is "Does G...
A k-separated matching in a graph is a set of edges at distance at least k from one another (hence, for instance, a 1-separated matching is just a matching in the classical sense)...
This paper proposes a method for reducing the maximum degree of vertices in graphs that maintain optimal broadcast time when a vertex can call a vertex at distance at most k durin...