Local Topological Toughness and Local Factors

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 edgetoughness 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. 1 Preliminaries and Results For notations not defined here we refer to [2]. Unless otherwise stated, t is an arbitrary non negative real number, k is an arbitrary integer, G is an arbitrary finite graph (loops and multiple edges allowed), U is an arbitrary subgraph of G, X and H are arbitrary disjoint subsets of V (G), Y is an arbitrary subset of E(G − X − H), and f is an arbitrary function that maps H into the positive integers. A cycle covering H is called H-cycle. The union of interna...

• Type: Journal
• Year: 2007
• Where: GC
• Authors: Frank Göring, Gyula Y. Katona
• Keywords: Applied Computing, GC 2007, Katona’s Idea, Local Topological Toughness, Topological Toughness