Premium
The longest cycle of a graph with a large minimal degree
Author(s) -
Alon Noga
Publication year - 1986
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.3190100115
Subject(s) - combinatorics , mathematics , conjecture , graph , hamiltonian path , degree (music) , cubic graph , discrete mathematics , line graph , voltage graph , physics , acoustics
We show that every graph G on n vertices with minimal degree at least n/k contains a cycle of length at least [ n /( k − 1)]. This verifies a conjecture of Katchalski. When k = 2 our result reduces to the classical theorem of Dirac that asserts that if all degrees are at least 1/2 n then G is Hamiltonian.
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom