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.

Rights

URN

URN:NBN:SI:DOC-LJCTN6IT

COBISSID

16795737

Added

29.05.2020

Metadata

Citation

APA:

Hellmuth, Marc, Leydold, Josef, Stadler, Peter F. (2014). Convex cycle bases. Ars mathematica contemporanea, volume 7, issue 1, str. 123-140. URN:NBN:SI:DOC-LJCTN6IT from http://www.dlib.si

MLA:

Hellmuth, Marc, Leydold, Josef, Stadler, Peter F.. "Convex cycle bases." Ars mathematica contemporanea volume 7. issue 1 (2014) str. 123-140.
<http://www.dlib.si/?URN=URN:NBN:SI:DOC-LJCTN6IT>

Ars mathematica contemporanea
2008-
(Assembly record)