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DC Field | Value | Language |
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dc.contributor.author | Borg, Peter | - |
dc.contributor.author | Fenech, Kurt | - |
dc.date.accessioned | 2021-05-17T07:26:23Z | - |
dc.date.available | 2021-05-17T07:26:23Z | - |
dc.date.issued | 2020 | - |
dc.identifier.citation | Borg, P., & Fenech, K. (2020). A Turán-type generalization of Tuza’s triangle edge cover problem. The Australasian Journal of Combinatorics, 78(3), 399-412. | en_GB |
dc.identifier.uri | https://www.um.edu.mt/library/oar/handle/123456789/75657 | - |
dc.description.abstract | We investigate the smallest number λk(G) of edges that can be removed from a non-empty graph G so that the resulting graph contains no kclique. Turán’s theorem tells us that λk(Kn) is the number of edges missing from the Turán graph T (n, k − 1). The investigation of λ3(G) was initiated by Tuza. Let G(k) be the union of k-cliques of G. Let m, t, and κ be the number of edges of G(k), the number of k-cliques of G, and ( k 2 ) , respectively. We prove that λk(G) ≤ 2m+κt 3κ , and that equality holds if and only if the k-cliques of G are pairwise edge-disjoint. We also prove that λk(G) ≤ m ( 1− (κ−1 κ )( κt ) 1 κ−1 ) , and this bound is also attained by unions of pairwise edge-disjoint k-cliques | en_GB |
dc.language.iso | en | en_GB |
dc.publisher | Centre for Discrete Mathematics & Computing | en_GB |
dc.rights | info:eu-repo/semantics/openAccess | en_GB |
dc.subject | Mathematics | en_GB |
dc.subject | Logic, Symbolic and mathematical | en_GB |
dc.subject | Set theory | en_GB |
dc.subject | Hypergraphs | en_GB |
dc.title | A Turán-type generalization of Tuza’s triangle edge cover problem | en_GB |
dc.type | article | en_GB |
dc.rights.holder | The copyright of this work belongs to the author(s)/publisher. The rights of this work are as defined by the appropriate Copyright Legislation or as modified by any successive legislation. Users may access this work and can make use of the information contained in accordance with the Copyright Legislation provided that the author must be properly acknowledged. Further distribution or reproduction in any format is prohibited without the prior permission of the copyright holder. | en_GB |
dc.description.reviewed | peer-reviewed | en_GB |
dc.publication.title | The Australasian Journal of Combinatorics | en_GB |
Appears in Collections: | Scholarly Works - FacSciMat |
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File | Description | Size | Format | |
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A_Turan-type_generalization_of_Tuzas_triangle_edge_cover_problem_2020.pdf | 175.22 kB | Adobe PDF | View/Open |
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