Second Hamiltonian Cycles in Claw-Free Graphs

Sheehan conjectured in 1975 that every Hamiltonian regular simple graph of even degree at least four contains a second Hamiltonian cycle. We prove that most claw-free Hamiltonian graphs with minimum degree at least 3 have a second Hamiltonian cycle and describe the structure of those graphs not cove...

Full description

Bibliographic Details
Main Authors:	Hossein Esfandiari, Colton Magnant, Pouria Salehi Nowbandegani, Shirdareh Haghighi
Format:	Article
Language:	English
Published:	Georgia Southern University 2015-01-01
Series:	Theory and Applications of Graphs
Subjects:	claw-free graph Sheehan’s conjecture second Hamiltonian cycle
Online Access:	https://digitalcommons.georgiasouthern.edu/tag/vol2/iss1/2

id	doaj-8af96b5d9ce0452484fc2cc250fa8ca2
record_format	Article
spelling	doaj-8af96b5d9ce0452484fc2cc250fa8ca22020-11-24T23:39:17ZengGeorgia Southern UniversityTheory and Applications of Graphs2470-98592015-01-012110.20429/tag.2015.020102Second Hamiltonian Cycles in Claw-Free GraphsHossein EsfandiariColton MagnantPouria Salehi NowbandeganiShirdareh HaghighiSheehan conjectured in 1975 that every Hamiltonian regular simple graph of even degree at least four contains a second Hamiltonian cycle. We prove that most claw-free Hamiltonian graphs with minimum degree at least 3 have a second Hamiltonian cycle and describe the structure of those graphs not covered by our result. By this result, we show that Sheehan’s conjecture holds for claw-free graphs whose order is not divisible by 6. In addition, we believe that the structure that we introduce can be useful for further studies on claw-free graphs.https://digitalcommons.georgiasouthern.edu/tag/vol2/iss1/2claw-free graphSheehan’s conjecturesecond Hamiltonian cycle
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Hossein Esfandiari Colton Magnant Pouria Salehi Nowbandegani Shirdareh Haghighi
spellingShingle	Hossein Esfandiari Colton Magnant Pouria Salehi Nowbandegani Shirdareh Haghighi Second Hamiltonian Cycles in Claw-Free Graphs Theory and Applications of Graphs claw-free graph Sheehan’s conjecture second Hamiltonian cycle
author_facet	Hossein Esfandiari Colton Magnant Pouria Salehi Nowbandegani Shirdareh Haghighi
author_sort	Hossein Esfandiari
title	Second Hamiltonian Cycles in Claw-Free Graphs
title_short	Second Hamiltonian Cycles in Claw-Free Graphs
title_full	Second Hamiltonian Cycles in Claw-Free Graphs
title_fullStr	Second Hamiltonian Cycles in Claw-Free Graphs
title_full_unstemmed	Second Hamiltonian Cycles in Claw-Free Graphs
title_sort	second hamiltonian cycles in claw-free graphs
publisher	Georgia Southern University
series	Theory and Applications of Graphs
issn	2470-9859
publishDate	2015-01-01
description	Sheehan conjectured in 1975 that every Hamiltonian regular simple graph of even degree at least four contains a second Hamiltonian cycle. We prove that most claw-free Hamiltonian graphs with minimum degree at least 3 have a second Hamiltonian cycle and describe the structure of those graphs not covered by our result. By this result, we show that Sheehan’s conjecture holds for claw-free graphs whose order is not divisible by 6. In addition, we believe that the structure that we introduce can be useful for further studies on claw-free graphs.
topic	claw-free graph Sheehan’s conjecture second Hamiltonian cycle
url	https://digitalcommons.georgiasouthern.edu/tag/vol2/iss1/2
work_keys_str_mv	AT hosseinesfandiari secondhamiltoniancyclesinclawfreegraphs AT coltonmagnant secondhamiltoniancyclesinclawfreegraphs AT pouriasalehinowbandegani secondhamiltoniancyclesinclawfreegraphs AT shirdarehhaghighi secondhamiltoniancyclesinclawfreegraphs
_version_	1725514246950748160

Second Hamiltonian Cycles in Claw-Free Graphs

Similar Items