Decomposing Graphs With Two Associate Classes Into Paths Of Length 3 And The Intersection Problem Of Latin Rectangles

Abstract

In this thesis, the decomposition problem of graphs with two associate classes into paths of length 3 is completely settled. The intersection problem for latin rectangles is completely solved as well. In addition, an Euler circuit of K(n, p) with diameter at least (n−3)p/2+1 is constructed and the intersection problem of latin squares of order n and n+1 is discussed.