On the CNF-complexity of bipartite graphs containing no squares

By a probabilistic construction, we find a bipartite graph having average degree d which can be expressed as a conjunctive normal form using C log d clauses. This negatively resolves Research Problem 1.33 of Jukna [S. Jukna, Boolean Function Complexity: Advances and Frontiers , Algorithms Comb., Vol...

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Vydané v:Lithuanian mathematical journal Ročník 52; číslo 4; s. 385 - 389
Hlavný autor: Katz, Nets Hawk
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Boston Springer US 01.10.2012
Predmet:
Actuarial Sciences
Mathematics
Mathematics and Statistics
Number Theory
Ordinary Differential Equations
Probability Theory and Stochastic Processes
Squares
graph complexity
probabilistic construction
05C80
ISSN:0363-1672, 1573-8825
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Shrnutí:By a probabilistic construction, we find a bipartite graph having average degree d which can be expressed as a conjunctive normal form using C log d clauses. This negatively resolves Research Problem 1.33 of Jukna [S. Jukna, Boolean Function Complexity: Advances and Frontiers , Algorithms Comb., Vol. 27, Springer, Berlin, Heidelberg, 2012].
ISSN:0363-1672
1573-8825
DOI:10.1007/s10986-012-9181-5