Quasigraphs and skeletal partitions
Tom\'a\v{s} Kaiser, Petr Vr\'ana
TL;DR
This paper presents a simplified and stronger proof of the Skeletal Lemma, a key tool for analyzing Hamilton cycles in line graphs, extending concepts from graphs to 3-hypergraphs.
Contribution
It provides a new, more accessible proof of the Skeletal Lemma, generalizing disjoint spanning trees results to 3-hypergraphs and enhancing its applicability.
Findings
Simplified proof of the Skeletal Lemma
Generalization to 3-hypergraphs
Stronger version suitable for applications
Abstract
We give a new proof of the Skeletal Lemma, which is the main technical tool in our paper on Hamilton cycles in line graphs [T. Kaiser and P. Vr\'ana, Hamilton cycles in 5-connected line graphs, European J. Combin. 33 (2012), 924-947]. It generalises results on disjoint spanning trees in graphs to the context of 3-hypergraphs. The lemma is proved in a slightly stronger version that is more suitable for applications. The proof is simplified and formulated in a more accessible way.
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Taxonomy
Topicsgraph theory and CDMA systems · Limits and Structures in Graph Theory · Graph theory and applications