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Abstract:
An r-uniform hypergraph is linear if every two edges intersect in at most one vertex. Given a family of r-uniform hypergraphs F, the linear Turan number exlin r (n, F) is the maximum number of edges of a linear r-uniform hypergraph on n vertices that does not contain any member of F as a subgraph. Let Kl be a complete graph with l vertices and r 2. The r-expansion of Kl is the r-graph Kl+ obtained from Kl by enlarging each edge of Kl with a vertex set of size r - 2 disjoint from V(Kl) such that distinct edges of Kl are enlarged by disjoint sets. Let T2(n, l) be the Turan graph, i.e., almost balanced complete l-partite graph with n vertices. When l r 3 and n is sufficiently large, we prove the following extension of Turan's Theorem exlin!n, K+" " |T2(n, l)| r " , l+1 !r 2 with equality holds if and only if there exist almost balanced l-partite r-graphs such that each pair of vertices from distinct parts are contained in one hyperedge exactly. Moreover, some results on linear Turan number of general configurations are also presented.
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ELECTRONIC JOURNAL OF COMBINATORICS
ISSN: 1077-8926
Year: 2022
Issue: 4
Volume: 29
Page: 1-12
0 . 7
JCR@2022
0 . 7 0 0
JCR@2023
ESI Discipline: MATHEMATICS;
ESI HC Threshold:24
JCR Journal Grade:3
CAS Journal Grade:4
Cited Count:
WoS CC Cited Count: 1
SCOPUS Cited Count: 1
ESI Highly Cited Papers on the List: 0 Unfold All
WanFang Cited Count:
Chinese Cited Count:
30 Days PV: 0
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