Göring, Frank ; Katona, Gyula Y. : Local topological toughness and local factors

Author(s):

Göring, Frank
Katona, Gyula Y.

Title:

Local topological toughness and local factors

Electronic source:

application/pdf

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 24, 2006

Mathematics Subject Classification:

05C38

[ Paths and cycles ]

Abstract:

We localize and strengthen Katona's idea of an edge-toughness to a local topological toughness. We disprove a conjecture of Katona concerning the connection between edge-toughness and factors. For the topological toughness we prove a theorem similar to Katona's 2k-factor-conjecture, which turned out to be false for his edge-toughness. We prove, that besides this the topological toughness has nearly all known nice properties of Katona's edge-toughness and therefore is worth to be considered.

Keywords:

graph, toughness, factor, H-path, hamiltonicity

Language:

English

Publication time:

10 / 2007