@article{b618479e197e40b79d59f5edde85c0be,
title = "Degree sums for edges and cycle lengths in graphs",
abstract = "Let G be a graph of order n satisfying d(u) + d(v) n for every edge uv of G. We show that the circumference - the length of a longest cycle - of G can be expressed in terms of a certain graph parameter, and can be computed in polynomial time. Moreover, we show that G contains cycles of every length between 3 and the circumference, unless G is complete bipartite. If G is 1-tough then it is pancyclic or G = Kr,r with r = n/2.",
keywords = "Circumference, Closure, Cycle, Graph, Degree, Pancyclic, Sum, Tough, Hamiltonian",
author = "Stephan Brandt and Veldman, {Henk Jan}",
year = "1997",
doi = "10.1002/(SICI)1097-0118(199708)25:4<253::AID-JGT2>3.0.CO;2-J",
language = "English",
volume = "25",
pages = "253--256",
journal = "Journal of graph theory",
issn = "0364-9024",
publisher = "Wiley",
number = "4",
}