Graph invariants and large cycles: a survey
type: Item
instance of: scholarly article
title: Graph invariants and large cycles: a survey
zbMATH Open document ID: 1213.05221
DOI: 10.1155/2011/206404
author: Zh. G. Nikoghosyan
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2011-05-27T00:00:00Z
full work available at URL: https://eudml.org/doc/228120
review text: Summary: Graph invariants provide a powerful analytical tool for investigation of abstract substructures of graphs. This paper is devoted to large cycle substructures, namely, Hamilton, longest and dominating cycles and some generalized cycles including Hamilton and dominating cycles as special cases. In this paper, we have collected 36 pure algebraic relations between basic (initial) graph invariants ensuring the existence of a certain type of large cycles. These simplest kind of relations having no forerunners in the area actually form a source from which nearly all possible hamiltonian results (including well-known Ore's theorem, Posa's theorem, and many other generalizations) can be developed further by various additional new ideas, generalizations, extensions, restrictions, and structural limitations.
Mathematics Subject Classification ID: 05C75
Mathematics Subject Classification ID: 05C38
Mathematics Subject Classification ID: 05C45
Mathematics Subject Classification ID: 05C69
zbMATH DE Number: 5900712
MaRDI profile type: Publication
OpenAlex ID: W1970942250
Wikidata QID: Q58687672
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description: scientific article; zbMATH DE number 5900712