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> Falgas Ravry Victor
> Zhao Yi >
Triangle-degrees in...
Triangle-degrees in graphs and tetrahedron coverings in 3-graphs
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- Falgas-Ravry, Victor (author)
- Umeå universitet,Institutionen för matematik och matematisk statistik
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- Markström, Klas (author)
- Umeå universitet,Institutionen för matematik och matematisk statistik
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Zhao, Yi (author)
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(creator_code:org_t)
- Cambridges Institutes Press, 2021
- 2021
- English.
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In: Combinatorics, probability & computing. - : Cambridges Institutes Press. - 0963-5483 .- 1469-2163. ; 30:2, s. 175-199
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Abstract
Subject headings
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- We investigate a covering problem in 3-uniform hypergraphs (3-graphs): Given a 3-graph F, what is c(1)(n, F), the least integer d such that if G is an n-vertex 3-graph with minimum vertex-degree delta(1)(G) > d then every vertex of G is contained in a copy of F in G?We asymptotically determine c(1)(n, F) when F is the generalized triangle K-4((3)), and we give close to optimal bounds in the case where F is the tetrahedron K-4((3)) (the complete 3-graph on 4 vertices).This latter problem turns out to be a special instance of the following problem for graphs: Given an nvertex graph G with m> n(2)/4 edges, what is the largest t such that some vertex in G must be contained in t triangles? We give upper bound constructions for this problem that we conjecture are asymptotically tight. We prove our conjecture for tripartite graphs, and use flag algebra computations to give some evidence of its truth in the general case.
Subject headings
- NATURVETENSKAP -- Matematik -- Diskret matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Discrete Mathematics (hsv//eng)
- NATURVETENSKAP -- Data- och informationsvetenskap -- Datavetenskap (hsv//swe)
- NATURAL SCIENCES -- Computer and Information Sciences -- Computer Sciences (hsv//eng)
Publication and Content Type
- ref (subject category)
- art (subject category)
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