Open AccessTwo Sufficient Conditions for Hamilton and Dominating Cycles
Author(s) -
Zh. G. Nikoghosyan
Publication year - 2012
Publication title -
international journal of mathematics and mathematical sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 39
eISSN - 1687-0425
pISSN - 0161-1712
DOI - 10.1155/2012/185346
Subject(s) - scalable vector graphics , combinatorics , mathematics , path (computing) , graph , computer science , world wide web , programming language
We prove that if is a 2-connect graph of size (the number of edges) and minimum degree with , where when and when , then each longest cycle in is a dominating cycle. The exact analog of this theorem for Hamilton cycles follows easily from two known results according to Dirac and Nash-Williams: each graph with is hamiltonian. Both results are sharp in all respects
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