Weighted maximum matchings and optimal equi-difference conflict-avoiding codes

Abstract

A conflict-avoiding code (CAC) of length and weight is a collection of -subsets of such that for any and , where . Let denote the class of all CACs of length and weight . A CAC is said to be equi-difference if any codeword has the form . A CAC with maximum size is called optimal. In this paper we propose a graphical characterization of an equi-difference CAC, and then provide an infinite number of optimal equi-difference CACs for weight four.