Note: The Smallest Nonevasive Graph Property

• Autorzy: Michał Adamaszek
• Języki publikacji: EN

Abstrakty

EN

A property of n-vertex graphs is called evasive if every algorithm testing this property by asking questions of the form “is there an edge between vertices u and v” requires, in the worst case, to ask about all pairs of vertices. Most “natural” graph properties are either evasive or conjectured to be such, and of the few examples of nontrivial nonevasive properties scattered in the literature the smallest one has n = 6. We exhibit a nontrivial, nonevasive property of 5-vertex graphs and show that it is essentially the unique such with n ≤ 5.

Słowa kluczowe

EN

graph properties; evasiveness; complexity.

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2014
• Tom: 34
• Numer: 4
• Strony: 857-862

Daty

wydano

2014-11-01

otrzymano

2013-08-06

poprawiono

2013-11-06

zaakceptowano

2013-11-06

online

2014-11-15

Twórcy

autor

Michał Adamaszek

• Institute of Mathematics, University of Bremen Bibliothekstr. 1 28359 Bremen, Germany

Bibliografia

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• [4] D. Kozlov, Combinatorial Algebraic Topology (Algorithms and Computation in Mathematics, Vol. 21, Springer-Verlag Berlin Heidelberg, 2008).
• [5] M. de Longueville, A Course in Topological Combinatorics (Universitext, Springer New York, 2013).
• [6] L. Lovász and N. Young, Lecture Notes on Evasiveness of Graph Properties, Tech. Rep. CS-TR-317-91, Computer Science Dept., Princeton University, available from arxiv/0205031.
• [7] E.C. Milner and D.J.A. Welsh, On the computational complexity of graph theoretical properties, Proc. 5th British Comb. Conf. Aberdeen 1975 (1976) 471-487.
• [8] The On-Line Encyclopedia of Integer Sequences, published electronically at oeis.org.
• [9] V. Welker, Constructions preserving evasiveness and collapsibility, Discrete Math. 207 (1999) 243-255. doi:10.1016/S0012-365X(99)00049-7

Identyfikatory

DOI

10.7151/dmgt.1766