Abstract
The edge coloring problem finds an assignment of colors to the edges of a given graph using as few colors as possible, so that no two adjacent edges receive the same colors. This problem arises in many application settings. Examples are routing in a permutation network, a preemptive scheduling of an open shop, a preemptive scheduling of unrelated parallel processors, and a class-teacher timetable problem. When a given graph is bipartite, strongly polynomial time algorithms for finding an edge coloring have previously been given.
In this paper, we propose an algorithm for finding all the edge colorings of bipartite graphs without parallel edges. Our algorithm requires O (Km(d*+logn)) time and O (d*m2) space, where n (m) denotes the number of vertices (edges), d* denotes the maximum degree, and K denotes the number of edge colorings. Although the time complexity is proportional to the number of edge colorings, the memory space doesn't depend on-it.
