Convex cycle bases

Marc Hellmuth, Josef Leydold, Peter F. Stadler
2013 Ars Mathematica Contemporanea  
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
more » ... bases that includes partial cubes and hence median graphs.
doi:10.26493/1855-3974.226.0a2 fatcat:2ftt4oixtfcsrfkcema5p6osfy