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Computation of the Folkman number F e (3, 3; 5)
Author(s) -
Piwakowski Konrad,
Radziszowski Stanisaw P.,
Urbański Sebastian
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(199909)32:1<41::aid-jgt4>3.0.co;2-p
Subject(s) - enumeration , vertex (graph theory) , combinatorics , computation , graph , mathematics , upper and lower bounds , enhanced data rates for gsm evolution , discrete mathematics , graph theory , computer science , theoretical computer science , algorithm , artificial intelligence , mathematical analysis
With the help of computer algorithms, we improve the lower bound on the edge Folkman number F e (3, 3; 5) and vertex Folkman number F v (3, 3; 4), and, thus, show that the exact values of these numbers are 15 and 14, respectively. We also present computer enumeration of all critical graphs. © 1999 John Wiley & Sons, Inc. J Graph Theory 32: 41–49, 1999