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On supercompact graphs
Author(s) -
Lim ChongKeang
Publication year - 1978
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.3190020410
Subject(s) - mathematics , combinatorics , clique graph , discrete mathematics , graph , split graph , block graph , clique , chordal graph , 1 planar graph , line graph , graph power
A graph G is called a supercompact graph if G is the intersection graph of some family of subsets of a set X such that satisfies the Helly property and for any x ≠ y in X , there exists S ∈ with x ∈ S , y ∉ S . Various characterizations of supercompact graphs are given. It is shown that every clique‐critical graph is supercompact. Furthermore, for any finite graph, H , there is at most a finite number of different supercompact graphs G such that H is the clique‐graph of G .
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