On a perfect problem

• Autorzy: Igor E. Zverovich
• Języki publikacji: EN

Abstrakty

EN

We solve Open Problem (xvi) from Perfect Problems of Chvátal [1] available at ftp://dimacs.rutgers.edu/pub/perfect/problems.tex: Is there a class C of perfect graphs such that
(a) C does not include all perfect graphs and
(b) every perfect graph contains a vertex whose neighbors induce a subgraph that belongs to C?
A class P is called locally reducible if there exists a proper subclass C of P such that every graph in P contains a local subgraph belonging to C. We characterize locally reducible hereditary classes. It implies that there are infinitely many solutions to Open Problem (xvi). However, it is impossible to find a hereditary class C of perfect graphs satisfying both (a) and (b).

Słowa kluczowe

EN

hereditary classes; perfect graphs

Kategorie tematyczne

• 05C17: Perfect graphs

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2006
• Tom: 26
• Numer: 2
• Strony: 273-277

Daty

wydano

2006

otrzymano

2005-09-06

poprawiono

2006-03-15

Twórcy

autor

Igor E. Zverovich

• RUTCOR - Rutgers Center for Operations Research, Rutgers, The State University of New Jersey, 640 Bartholomew Road, Piscataway, NJ 08854-8003, USA

Bibliografia

• [1] V. Chvátal, Perfect Problems, available at http://www.cs.concordia.ca/∼chvatal/perfect/problems.html.
• [2] G.A. Dirac, On rigid circuit graphs, Abh. Math. Semin. Univ. Hamburg 25 (1961) 71-76, doi: 10.1007/BF02992776.
• [3] Perfect graphs, Edited by J.L. Ramírez Alfonsín and B.A. Reed, Wiley-Interscience Series in Discrete Mathematics and Optimization (John Wiley & Sons, Ltd., Chichester, 2001) xxii+362 pp.
• [4] A.A. Zykov, Fundamentals of Graph Theory (Nauka, Moscow, 1987) 382 pp. (in Russian), translated and edited by L. Boron, C. Christenson and B. Smith (BCS Associates, Moscow, ID, 1990) vi+365 pp.

Identyfikatory

DOI

10.7151/dmgt.1318