The Bounds of the Edge Number in Generalized Hypertrees
School of Computer, Qinghai Normal University, Xining 810008, China
Key Laboratory of Tibetan Information Processing and Machine Translation in QH, Xining 810008, China
Key Laboratory of the Education Ministry for Tibetan Information Processing, Xining 810008, China
School of Computer Science, Shannxi Normal university, Xi’an 710062, China
School of mathematics and statistics, Qinghai Normal University, Xining 810008, China
Author to whom correspondence should be addressed.
Received: 11 November 2018 / Revised: 14 December 2018 / Accepted: 15 December 2018 / Published: 20 December 2018
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is a pair consisting of a vertex set
, and a set
of subsets (the hyperedges of
. A hypergraph
-uniform if all the hyperedges of
have the same cardinality
-uniform hypergraph, we generalize the concept of trees for
-uniform hypergraphs. We say that an
is a generalized hypertree (
is disconnected after removing any hyperedge
, and the number of components of
is a fixed value
. We focus on the case that
has exactly two components. An edge-minimal
whose edge set is minimal with respect to inclusion. After considering these definitions, we show that an
vertices has at least
edges and it has at most
, and the lower and upper bounds on the edge number are sharp. We then discuss the case that
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MDPI and ACS Style
Zhang, K.; Zhao, H.; Ye, Z.; Zhu, Y.; Wei, L. The Bounds of the Edge Number in Generalized Hypertrees. Mathematics 2019, 7, 2.
Zhang K, Zhao H, Ye Z, Zhu Y, Wei L. The Bounds of the Edge Number in Generalized Hypertrees. Mathematics. 2019; 7(1):2.
Zhang, Ke; Zhao, Haixing; Ye, Zhonglin; Zhu, Yu; Wei, Liang. 2019. "The Bounds of the Edge Number in Generalized Hypertrees." Mathematics 7, no. 1: 2.
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