TY - CHAP

T1 - The deficiency of a hypergraph

AU - Henning, Michael A.

AU - Yeo, Anders

N1 - Publisher Copyright:
© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020.

PY - 2020

Y1 - 2020

N2 - In this chapter, we introduce the completely new technique of the deficiency of a hypergraph. Using this concept of deficiency, we prove here a key theorem that we will need in establishing the transversal number of a linear 4-uniform hypergraph, including determining the Tuza constant q4 in the next chapter. We begin this chapter by defining a few so-called special hypergraphs. We then introduce the concept of the deficiency of a set of hypergraphs. Thereafter, we prove a key theorem that we will need in establishing the transversal number of a linear 4-uniform hypergraph. Throughout this section, we let L4, 3 be the class of all 4-uniform, linear hypergraphs with maximum degree at most 3. Thus, L4, 3 is a subclass of the class L4 of all 4-uniform, linear hypergraphs.

AB - In this chapter, we introduce the completely new technique of the deficiency of a hypergraph. Using this concept of deficiency, we prove here a key theorem that we will need in establishing the transversal number of a linear 4-uniform hypergraph, including determining the Tuza constant q4 in the next chapter. We begin this chapter by defining a few so-called special hypergraphs. We then introduce the concept of the deficiency of a set of hypergraphs. Thereafter, we prove a key theorem that we will need in establishing the transversal number of a linear 4-uniform hypergraph. Throughout this section, we let L4, 3 be the class of all 4-uniform, linear hypergraphs with maximum degree at most 3. Thus, L4, 3 is a subclass of the class L4 of all 4-uniform, linear hypergraphs.

UR - http://www.scopus.com/inward/record.url?scp=85089507492&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-46559-9_8

DO - 10.1007/978-3-030-46559-9_8

M3 - Chapter

AN - SCOPUS:85089507492

T3 - Developments in Mathematics

SP - 53

EP - 135

BT - Developments in Mathematics

PB - Springer

ER -