Efficient algorithms for decomposing graphs under degree constraints |
| |
Authors: | Cristina Bazgan Daniel Vanderpooten |
| |
Institution: | a LAMSADE, Université Paris-Dauphine, Place du Marechal de Lattre de Tassigny, 75775 Paris Cedex 16, France b Computer and Automation Institute, Hungarian Academy of Sciences, Budapest, Hungary c Department of Computer Science, University of Pannonia, Veszprém, Hungary |
| |
Abstract: | Stiebitz Decomposing graphs under degree constraints, J. Graph Theory 23 (1996) 321-324] proved that if every vertex v in a graph G has degree d(v)?a(v)+b(v)+1 (where a and b are arbitrarily given nonnegative integer-valued functions) then G has a nontrivial vertex partition (A,B) such that dA(v)?a(v) for every v∈A and dB(v)?b(v) for every v∈B. Kaneko On decomposition of triangle-free graphs under degree constraints, J. Graph Theory 27 (1998) 7-9] and Diwan Decomposing graphs with girth at least five under degree constraints, J. Graph Theory 33 (2000) 237-239] strengthened this result, proving that it suffices to assume d(v)?a+b (a,b?1) or just d(v)?a+b-1 (a,b?2) if G contains no cycles shorter than 4 or 5, respectively.The original proofs contain nonconstructive steps. In this paper we give polynomial-time algorithms that find such partitions. Constructive generalizations for k-partitions are also presented. |
| |
Keywords: | Graph decomposition Vertex partition Polynomial algorithm Vertex degree |
本文献已被 ScienceDirect 等数据库收录! |
|