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Graphs and Combinatorics

, Volume 35, Issue 1, pp 195–200 | Cite as

H-Decomposition of r-Graphs when H is an r-Graph with Exactly k Independent Edges

  • Xinmin HouEmail author
  • Boyuan Liu
  • Hongliang Lu
Original Paper
  • 44 Downloads

Abstract

Let \(\phi _H^r(n)\) be the smallest integer such that, for all r-graphs G on n vertices, the edge set E(G) can be partitioned into at most \(\phi _H^r(n)\) parts, of which every part either is a single edge or forms an r-graph isomorphic to H. The function \(\phi ^2_H(n)\) has been well studied in literature, but for the case \(r\ge 3\), the problem of determining \(\phi _H^r(n)\) is widely open. Sousa (Electron J Comb 17:R40, 2010) gave an asymptotic value of \(\phi _H^r(n)\) when H is an r-graph with exactly 2 edges, and determined the exact value of \(\phi _H^r(n)\) in some special cases. In this paper, we give the exact value of \(\phi _H^r(n)\) when H is an r-graph with exactly 2 edges, which completes Sousa’s result, we further determine the exact value of \(\phi _H^r(n)\) when H is an r-graph consisting of exactly k independent edges.

Keywords

Hypergraph Decomposition Independent edges 

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Copyright information

© Springer Japan KK, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Key Laboratory of Wu Wen-Tsun Mathematics, School of Mathematical SciencesUniversity of Science and Technology of ChinaHefeiChina
  2. 2.School of Mathematics and StatisticsXi’an Jiaotong UniversityXi’anChina

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