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On the minimum size of tight hypergraphs
Author(s) -
Arocha Jorge L.,
Bracho Javier,
NeumannLara Victor
Publication year - 1992
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.3190160405
Subject(s) - combinatorics , injective function , mathematics , conjecture , surjective function , graph , discrete mathematics
Abstract A k ‐graph, H = ( V, E ), is tight if for every surjective mapping f : V → {1,….k} there exists an edge α ϵ E sicj tjat f | α is injective. Clearly, 2‐graphs are tight if and only if they are connected. Bounds for the minimum number ϕ n kof edges in a tight k ‐graph with n vertices are given. We conjecture that ϕ n 3for every n and prove the equality when 2 n + 1 is prime. From the examples, minimal embeddings of complete graphs into surfaces follow. © 1992 John Wiley & Sons, Inc.