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Hajós constructions of critical graphs
Author(s) -
Jensen Tommy R.,
Royle Gordon F.
Publication year - 1999
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/(sici)1097-0118(199901)30:1<37::aid-jgt5>3.0.co;2-v
Subject(s) - combinatorics , mathematics , graph , discrete mathematics
For every k ≥ 4 there exists a k ‐critical graph that is not Hajós‐ k ‐constructible through a sequence of k ‐critical graphs. This completely answers a question of G. Hajós, which has been answered previously only for k = 8 with an example given by P. Catlin. Also the corresponding problem for Ore's construction has the analogous answer for all k ≥ 4. © 1999 John Wiley & Sons, Inc. J Graph Theory 30: 37–5, 1999