Abstract. For each r-regular graph G, define a binary sequence O(G) = (01,02 ..... 0,-1) by 0 k = 0 ifG has a k-factor, and 0 k --1 otherwise. A binary sequence e = (ei[i = 1,2,...,r -1) is said to be realizable if there exists an r-regular graph G such that O(G) = e. In this paper we characterize all binary sequences which are realizable.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.