TY - GEN

T1 - Deciding the Bell number for hereditary graph properties

AU - Atminas, Aistis

AU - Collins, Andrew

AU - Foniok, Jan

AU - Lozin, Vadim V.

N1 - Publisher Copyright:
© Springer International Publishing Switzerland 2014.

PY - 2014

Y1 - 2014

N2 - The paper [J. Balogh, B. Bollobás, D. Weinreich, A jump to the Bell number for hereditary graph properties, J. Combin. Theory Ser. B 95 (2005) 29–48] identifies a jump in the speed of hereditary graph properties to the Bell number Bn and provides a partial characterisation of the family of minimal classes whose speed is at least Bn. In the present paper, we give a complete characterisation of this family. Since this family is infinite, the decidability of the problem of determining if the speed of a hereditary property is above or below the Bell number is questionable. We answer this question positively for properties defined by finitely many forbidden induced subgraphs. In other words, we show that there exists an algorithm which, given a finite set F of graphs, decides whether the speed of the class of graphs containing no induced subgraphs from the set F is above or below the Bell number.

AB - The paper [J. Balogh, B. Bollobás, D. Weinreich, A jump to the Bell number for hereditary graph properties, J. Combin. Theory Ser. B 95 (2005) 29–48] identifies a jump in the speed of hereditary graph properties to the Bell number Bn and provides a partial characterisation of the family of minimal classes whose speed is at least Bn. In the present paper, we give a complete characterisation of this family. Since this family is infinite, the decidability of the problem of determining if the speed of a hereditary property is above or below the Bell number is questionable. We answer this question positively for properties defined by finitely many forbidden induced subgraphs. In other words, we show that there exists an algorithm which, given a finite set F of graphs, decides whether the speed of the class of graphs containing no induced subgraphs from the set F is above or below the Bell number.

UR - http://www.scopus.com/inward/record.url?scp=84909578578&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-12340-0_6

DO - 10.1007/978-3-319-12340-0_6

M3 - Conference Proceeding

AN - SCOPUS:84909578578

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 69

EP - 80

BT - Graph-Theoretic Concepts in Computer Science - 40th International Workshop, WG 2014, Revised Selected Papers

A2 - Kratsch, Dieter

A2 - Todinca, Ioan

PB - Springer Verlag

T2 - 40th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2014

Y2 - 25 June 2014 through 27 June 2014

ER -