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Bounding Mean Orders of Sub-k-Trees of k-Trees
Katholieke Univ Leuven, Dept Comp Sci, Campus Kulak, Kortrijk, Belgium..
Montana State Univ, Sch Comp, Bozeman, MT USA..
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Probability Theory and Combinatorics. Graz Univ Technol, Inst Discrete Math, Graz, Austria..ORCID iD: 0000-0001-5533-2764
Georgia Inst Technol, Sch Math, Atlanta, GA USA..ORCID iD: 0000-0003-3762-8865
2024 (English)In: The Electronic Journal of Combinatorics, ISSN 1097-1440, E-ISSN 1077-8926, Vol. 31, no 1, article id P1.62Article in journal (Refereed) Published
Abstract [en]

For a k-tree T, we prove that the maximum local mean order is attained in a k-clique of degree 1 and that it is not more than twice the global mean order. We also bound the global mean order if T has no k-cliques of degree 2 and prove that for large order, the k -star attains the minimum global mean order. These results solve the remaining problems of Stephens and Oellermann [J. Graph Theory 88 (2018), 61-79] concerning the mean order of sub-k-trees of k-trees.

Place, publisher, year, edition, pages
Electronic Journal of Combinatorics , 2024. Vol. 31, no 1, article id P1.62
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Probability Theory and Statistics
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URN: urn:nbn:se:uu:diva-526266DOI: 10.37236/12426ISI: 001189096800001OAI: oai:DiVA.org:uu-526266DiVA, id: diva2:1849690
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Swedish Research Council, 2022-04030Available from: 2024-04-08 Created: 2024-04-08 Last updated: 2024-04-08Bibliographically approved

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Wagner, Stephan

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