Edge-maximal <i>θ</i><sub>2k+1</sub>-free non-bipartite Hamiltonian graphs of odd order

Edge-maximal <i>θ</i><sub>2k+1</sub>-free non-bipartite Hamiltonian graphs of odd order

<p dir="ltr">Let ⁡(;<sub>2</sub><sub>⁢</sub><sub></sub><sub>+</sub><sub>1</sub>) denote the class of non-bipartite graphs on <i>n</i> vertices containing no <sub>2</sub><sub>⁢</sub><sub...

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محفوظ في:
التفاصيل البيبلوغرافية
المؤلف الرئيسي: M. M. M. Jaradat (14153370) (author)
مؤلفون آخرون: A. Baniabedalruhman (21606335) (author), M. S. Bataineh (21606338) (author), A. M. M. Jaradat (21606341) (author), A. A. Al-Rhayyel (21606344) (author)
منشور في: 2022
الموضوعات:
Mathematical sciences
Applied mathematics
Ramsey number
theta graph
complete graph
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author M. M. M. Jaradat (14153370)
author2 A. Baniabedalruhman (21606335)
M. S. Bataineh (21606338)
A. M. M. Jaradat (21606341)
A. A. Al-Rhayyel (21606344)
author2_role author
author
author
author
author_facet M. M. M. Jaradat (14153370)
A. Baniabedalruhman (21606335)
M. S. Bataineh (21606338)
A. M. M. Jaradat (21606341)
A. A. Al-Rhayyel (21606344)
author_role author
dc.creator.none.fl_str_mv M. M. M. Jaradat (14153370)
A. Baniabedalruhman (21606335)
M. S. Bataineh (21606338)
A. M. M. Jaradat (21606341)
A. A. Al-Rhayyel (21606344)
dc.date.none.fl_str_mv 2022-11-15T09:00:00Z
dc.identifier.none.fl_str_mv 10.1080/09728600.2022.2145922
dc.relation.none.fl_str_mv https://figshare.com/articles/journal_contribution/Edge-maximal_i_i_sub_2k_1_sub_-free_non-bipartite_Hamiltonian_graphs_of_odd_order/29413454
dc.rights.none.fl_str_mv CC BY 4.0
info:eu-repo/semantics/openAccess
dc.subject.none.fl_str_mv Mathematical sciences
Applied mathematics
Ramsey number
theta graph
complete graph
dc.title.none.fl_str_mv Edge-maximal <i>θ</i><sub>2k+1</sub>-free non-bipartite Hamiltonian graphs of odd order
dc.type.none.fl_str_mv Text
Journal contribution
info:eu-repo/semantics/publishedVersion
text
contribution to journal
description <p dir="ltr">Let ⁡(;<sub>2</sub><sub>⁢</sub><sub></sub><sub>+</sub><sub>1</sub>) denote the class of non-bipartite graphs on <i>n</i> vertices containing no <sub>2</sub><sub>⁢</sub><sub></sub><sub>+</sub><sub>1</sub>-graph and ⁡(;<sub>2</sub><sub>⁢</sub><sub></sub><sub>+</sub><sub>1</sub>)=max⁡{ℰ⁡():∈⁡(;<sub>2</sub><sub>⁢</sub><sub></sub><sub>+</sub><sub>1</sub>)}. Let ℋ⁡(;<sub>2</sub><sub>⁢</sub><sub></sub><sub>+</sub><sub>1</sub>) denote the class of non-bipartite Hamiltonian graphs on <i>n</i> vertices containing no <sub>2</sub><sub>⁢</sub><sub></sub><sub>+</sub><sub>1</sub>-graph and ℎ⁡(;<sub>2</sub><sub>⁢</sub><sub></sub><sub>+</sub><sub>1</sub>)=max⁡{ℰ⁡():∈ℋ⁡(;<sub>2</sub><sub>⁢</sub><sub></sub><sub>+</sub><sub>1</sub>)}. In this paper we determine ℎ⁡(;<sub>2</sub><sub>⁢</sub><sub></sub><sub>+</sub><sub>1</sub>) by proving that for sufficiently large odd <i>n</i>, ℎ⁡(;<sub>2</sub><sub>⁢</sub><sub></sub><sub>+</sub><sub>1</sub>)≤⌊(−2⁢+3)24⌋+2⁢−3. Furthermore, the bound is best possible. Our results confirm the conjecture made by Bataineh in 2007.</p><h2>Other Information</h2><p dir="ltr">Published in: AKCE International Journal of Graphs and Combinatorics<br>License: <a href="http://creativecommons.org/licenses/by/4.0/" target="_blank">http://creativecommons.org/licenses/by/4.0/</a><br>See article on publisher's website: <a href="https://dx.doi.org/10.1080/09728600.2022.2145922" target="_blank">https://dx.doi.org/10.1080/09728600.2022.2145922</a></p>
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network_acronym_str Manara2
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spelling Edge-maximal <i>θ</i><sub>2k+1</sub>-free non-bipartite Hamiltonian graphs of odd orderM. M. M. Jaradat (14153370)A. Baniabedalruhman (21606335)M. S. Bataineh (21606338)A. M. M. Jaradat (21606341)A. A. Al-Rhayyel (21606344)Mathematical sciencesApplied mathematicsRamsey numbertheta graphcomplete graph<p dir="ltr">Let ⁡(;<sub>2</sub><sub>⁢</sub><sub></sub><sub>+</sub><sub>1</sub>) denote the class of non-bipartite graphs on <i>n</i> vertices containing no <sub>2</sub><sub>⁢</sub><sub></sub><sub>+</sub><sub>1</sub>-graph and ⁡(;<sub>2</sub><sub>⁢</sub><sub></sub><sub>+</sub><sub>1</sub>)=max⁡{ℰ⁡():∈⁡(;<sub>2</sub><sub>⁢</sub><sub></sub><sub>+</sub><sub>1</sub>)}. Let ℋ⁡(;<sub>2</sub><sub>⁢</sub><sub></sub><sub>+</sub><sub>1</sub>) denote the class of non-bipartite Hamiltonian graphs on <i>n</i> vertices containing no <sub>2</sub><sub>⁢</sub><sub></sub><sub>+</sub><sub>1</sub>-graph and ℎ⁡(;<sub>2</sub><sub>⁢</sub><sub></sub><sub>+</sub><sub>1</sub>)=max⁡{ℰ⁡():∈ℋ⁡(;<sub>2</sub><sub>⁢</sub><sub></sub><sub>+</sub><sub>1</sub>)}. In this paper we determine ℎ⁡(;<sub>2</sub><sub>⁢</sub><sub></sub><sub>+</sub><sub>1</sub>) by proving that for sufficiently large odd <i>n</i>, ℎ⁡(;<sub>2</sub><sub>⁢</sub><sub></sub><sub>+</sub><sub>1</sub>)≤⌊(−2⁢+3)24⌋+2⁢−3. Furthermore, the bound is best possible. Our results confirm the conjecture made by Bataineh in 2007.</p><h2>Other Information</h2><p dir="ltr">Published in: AKCE International Journal of Graphs and Combinatorics<br>License: <a href="http://creativecommons.org/licenses/by/4.0/" target="_blank">http://creativecommons.org/licenses/by/4.0/</a><br>See article on publisher's website: <a href="https://dx.doi.org/10.1080/09728600.2022.2145922" target="_blank">https://dx.doi.org/10.1080/09728600.2022.2145922</a></p>2022-11-15T09:00:00ZTextJournal contributioninfo:eu-repo/semantics/publishedVersiontextcontribution to journal10.1080/09728600.2022.2145922https://figshare.com/articles/journal_contribution/Edge-maximal_i_i_sub_2k_1_sub_-free_non-bipartite_Hamiltonian_graphs_of_odd_order/29413454CC BY 4.0info:eu-repo/semantics/openAccessoai:figshare.com:article/294134542022-11-15T09:00:00Z
spellingShingle Edge-maximal <i>θ</i><sub>2k+1</sub>-free non-bipartite Hamiltonian graphs of odd order
M. M. M. Jaradat (14153370)
Mathematical sciences
Applied mathematics
Ramsey number
theta graph
complete graph
status_str publishedVersion
title Edge-maximal <i>θ</i><sub>2k+1</sub>-free non-bipartite Hamiltonian graphs of odd order
title_full Edge-maximal <i>θ</i><sub>2k+1</sub>-free non-bipartite Hamiltonian graphs of odd order
title_fullStr Edge-maximal <i>θ</i><sub>2k+1</sub>-free non-bipartite Hamiltonian graphs of odd order
title_full_unstemmed Edge-maximal <i>θ</i><sub>2k+1</sub>-free non-bipartite Hamiltonian graphs of odd order
title_short Edge-maximal <i>θ</i><sub>2k+1</sub>-free non-bipartite Hamiltonian graphs of odd order
title_sort Edge-maximal <i>θ</i><sub>2k+1</sub>-free non-bipartite Hamiltonian graphs of odd order
topic Mathematical sciences
Applied mathematics
Ramsey number
theta graph
complete graph

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