Estimations for the number of cycles in a graph
type: Item
instance of: scholarly article
title: Estimations for the number of cycles in a graph
zbMATH Open document ID: 0880.05057
DOI: 10.1007/BF02093512
author: Lutz Volkmann
published in: Periodica Mathematica Hungarica
publication date: 1998-01-07T00:00:00Z
review text: The paper offers some bounds on \(\nu(G)\), the number of cycles in an undirected graph \(G\). The bounds are mainly lower bounds, and in terms of \(\delta\), the minimal degree of the graph \(G\). For a loopless graph \(G\) we have \(\nu(G) \geq 1/2 \delta(\delta-1)\). If \(|V(G)|\geq 3\) and \(\delta \geq 5\) then \(\nu(G) \geq \delta(\delta-1)\), etc. There are even better bounds for special graphs, such as Hamiltonian or block graphs.
reviewed by: András Pluhár
Mathematics Subject Classification ID: 05C38
zbMATH DE Number: 1101399
zbMATH Keywords: undirected graph
zbMATH Keywords: cycle
zbMATH Keywords: minimum degree
zbMATH Keywords: Hamiltonian graphs
MaRDI profile type: Publication
cites work: Q3097395
cites work: Q3922712
cites work: Q5611646
cites work: On Algorithms for Enumerating All Circuits of a Graph
cites work: Cycles in the complement of a tree
cites work: The maximum number of cycles in the complement of a tree
description: scientific article; zbMATH DE number 1101399