Open AccessBook
Hypergraphs: Combinatorics of Finite Sets
Claude Berge
- 11 Jul 2011
1K
TL;DR: This chapter discusses Hypergraphs Generalising Bipartite Graphs, which are a collection of hypergraphs designed to solve the problem of Uniform Colourings in Matroids, and some of the properties of these graphs.
read more
Abstract: 1. General Concepts. Dual Hypergraphs. Degrees. Intersecting Families. The Coloured Edge Property and Chvatal's Conjecture. The Helly Property. Section of a Hypergraph and the Kruskal-Katona Theorem. Conformal Hypergraphs. Representative Graphs. 2. Transversal Sets and Matchings. Transversal Hypergraphs. The Coefficients r and r'. r-Critical Hypergraphs. The Konig Property. 3. Fractional Transversals. Fractional Transversal Number. Fractional Matching of a Graph. Fractional Transversal Number of a Regularisable Hypergraph. Greedy Transversal Number. Ryser's Conjecture. Transversal Number of Product Hypergraphs. 4. Colourings. Chromatic Number. Particular Kinds of Colourings. Uniform Colourings. Extremal Problems Related to the Chromatic Number. Good Edge-Colourings of a Complete Hypergraph. An Application to an Extremal Problem. Kneser's Problem. 5. Hypergraphs Generalising Bipartite Graphs. Hypergraphs without Odd Cycles. Unimodular Hypergraphs. Balanced Hypergraphs. Arboreal Hypergraphs. Normal Hypergraphs. Mengerian Hypergraphs. Paranormal Hypergraphs. Appendix: Matchings and Colourings in Matroids. References.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
Relational Learning with Hypergraphs
Li Pu
- 01 Jan 2013
TL;DR: This paper presents a meta-analyses of relational learning, spectral graph theory, and recommender system for network traffic inspection at the Ecole polytechnique federale de Lausanne EPFL in 2013.
Towards hypergraph cognitive networks as feature-rich models of knowledge
TL;DR: In this paper , a higher-order cognitive hypergraph model was proposed to predict word concreteness in the Small World of Words corpus, where each concept is endowed with a vector of psycholinguistic features.
Computing knock-out strategies in metabolic networks.
TL;DR: An algorithm is described that computes both the knock-out sets and the elementary modes containing the blocked reactions directly from the description of the network and whose worst-case computational complexity is better than the algorithms currently in use for these problems.
Emerging cubes for trends analysis in OLAP databases
Sébastien Nedjar,Alain Casali,Rosine Cicchetti,Lotfi Lakhal +3 more
- 03 Sep 2007
TL;DR: This paper addresses the issue of performing cube comparisons in order to exhibit trend reversals between two cubes and introduces the concept of emerging cube, a condensed representation of emerging cubes which avoids to compute two underlying cubes.
The Influence of Hyperedge Uniformity on The Characteristics of Small-world Hypernetworks
TL;DR: Four types of small-world hypernetworks evolution model algorithms based on hypergraphs are constructed and it can be seen that, under the same conditions, small- worldhypernetworks with uniform hyperedges have the smallest average hyperpath length and the largest hyperedge aggregation coefficient.