Abstract
Convex cycles play a role e.g. in the context of product graphs. We introduce convex
cycle bases and describe a polynomial-time algorithm that recognizes whether a given
graph has a convex cycle basis and provides an explicit construction in the positive case.
Relations between convex cycles bases and other types of cycles bases are discussed. In
particular we show that if G has a unique minimal cycle bases, this basis is convex. Furthermore,
we characterize a class of graphs with convex cycles bases that includes partial
cubes and hence median graphs.
Citation
[HLS14] Hellmuth, M., Leydold, J., and Stadler, P.F.: Convex Cycle Bases, Ars Math. Contemporanea, 7, 1, 123-140, 2014.
