An Extremal Problem Resulting in Many Paths

Abstract

For a bipartite graph the extremal number for the existence of a specific odd (even) length path was determined in J. Graph Theory \(8 (1984), 83-95\). In this article, we conjecture that for a balanced bi-partite graph with partite sets of odd order the extremal number for an even order path guarantees many more paths of differing lengths.The conjecture is proved for a linear portion of the conjectured paths.