Premium
Fragments in k critical n ‐connected graphs
Author(s) -
Jianji Su
Publication year - 1995
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.3190200304
Subject(s) - combinatorics , mathematics , conjecture , disjoint sets , graph , cardinality (data modeling) , pairwise comparison , order (exchange) , discrete mathematics , cograph , chordal graph , 1 planar graph , computer science , statistics , finance , economics , data mining
Madar conjectured that every k ‐critical n ‐connected non‐complete graph G has (2 k + 2) pairwise disjoint fragments. We show that Mader's conjecture holds if the order of G is greater than ( k + 2) n . From this, it implies that two other conjectures on k ‐critical n ‐connected graphs posed by Entringer, Slater, and Mader also hold if the cardinality of the graphs is large. © 1995 John Wiley & Sons, Inc.