Journal or Publication Title:

Математические вопросы кибернетики и вычислительной техники=Կիբեռնետիկայի և հաշվողական տեխնիկայի մաթեմատիկական հարցեր=Mathematical problems of computer science

Date of publication:

2013

Volume:

40

ISSN:

0131-4645

Additional Information:

սեղմիր այստեղ կապին հետևելու համար

Other title:

Տրված կոշտությամբ ոչ համիլտոնյան գրաֆներ; Негамильтоновые графы с заданной жесткостью

Coverage:

13-22

Abstract:

In 1973, Chv¶atal introduced the concept of toughness ¿ of a graph and conjectured that there exists a ¯nite constant t0 such that every t0-tough graph (that is ¿ ¸ t0) is hamiltonian. To solve this challenging problem, all e®orts are directed towards constructing non-hamiltonian graphs with toughness as large as possible. The last result in this direction is due to Bauer, Broersma and Veldman, which states that for each positive ², there exists a non-hamiltonian graph with 9 4 ¡ ² · ¿ < 9 4. The following related broad-scale problem, reminding the well-known pancyclicity or hypohamiltonicity, arises naturally: whedher there exists a non-hamiltonian graph with a given toughness. We conjecture that if there exist a non-hamiltonian t-tough graph then for each rational number a with 0 < a · t there exists a non-hamiltonian graph whose toughness is exactly a. In this paper we prove this conjecture for t = 9 4 ¡ ² by using a number of additional modi¯ed building blocks to construct the required graphs.

Publisher:

Изд-во НАН РА

Date created:

2013-09-10

Format:

pdf

Identifier:

oai:arar.sci.am:258786

Location of original object:

ՀՀ ԳԱԱ Հիմնարար գիտական գրադարան