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On the distribution of cycle lengths in graphs
Author(s) -
Gyárfás A.,
Komlós J.,
Szemerédi E.
Publication year - 1984
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.3190080402
Subject(s) - mathematics , combinatorics , conjecture , graph , degree (music) , distribution (mathematics) , set (abstract data type) , constant (computer programming) , discrete mathematics , mathematical analysis , physics , computer science , acoustics , programming language
The set of different cycle lengths of a graph G is denoted by C ( G ). We study how the distribution of C ( G ) depends on the minimum degree of G . We prove two results indicating that C ( G ) is dense in some sense. These results lead to the solution of a conjecture of Erdös and Hajnal stating that for suitable positive constants a, b the following holds:where δ( G ) denotes the minimum degree of G .
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