List decomposition of graphs

Citations of this article
Mendeley users who have this article in their library.


A family of graphs possesses the common gcd property if the greatest common divisor of the degree sequence of each graph in the family is the same. In particular, any family of trees has the common gcd property. Let F = {H1,...,Hr} be a family of graphs having the common gcd property, and let d be the common gcd. It is proved that there exists a constant N = N(F) such that for every n > N for which d divides n -1, and for every equality of the form α1e(H1) +⋯+αre(Hr)= (n/2), where α1,...,αr are nonnegative integers, the complete graph Kn has a decomposition in which each Hi appears exactly αi times. In case F is a family of trees the bound N(F) is shown to be polynomial in the size of F, and, furthermore, a polynomial (in n) time algorithm which generates the required decomposition is presented. ©2002 Elsevier Science B.V. All rights reserved.

Author supplied keywords




Caro, Y., & Yuster, R. (2002). List decomposition of graphs. Discrete Mathematics, 243(1–3), 67–77.

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free