Journal of Combinatorics
Volume 3 (2012)
Partitioning graphs into paths or cycles of prescribed lengths
Pages: 135 – 161
In this paper, we consider the path (and cycle) partition problem for graphs with additional length restrictions. More specifically, we prove sufficient degree sum conditions for the vertices of a graph to be partitioned into paths, with fixed end vertices, such that these paths have approximately prescribed lengths. We also prove similar results for partitions into cycles of approximately prescribed lengths each containing a specified vertex.
graph partition, degree sum, path length
2010 Mathematics Subject Classification
Primary 05C70. Secondary 05C35.