Journal or Publication Title:

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

Date of publication:

2016

Volume:

46

ISSN:

0131-4645

Additional Information:

Նիկողոսյան Ժ., Никогосян Ж.

Other title:

Կմախքային ծառեր քիչ ճյուղային և կախված գագաթներով; Каркасы с менышим числом висячих и Br-вершин

Coverage:

18-25

Abstract:

For a graph G, let °² be the minimum degree sum of two nonadjacent vertices in G. A vertex of degree one in a tree is called an end vertex and a vertex of degree at least three is called a branch vertex. We consider: (*) connected graphs on n vertices such that °² ≥ n-k+1 for some positive integer k. In 1976, it was proved (by the author) that every graph satisfying (¤), has a spanning tree with at most k end vertices. In this paper we first show that every graph satisfying (*), has a spanning tree with at most k+1 branch and end vertices altogether. The next result states that every graph satisfying (¤), has a spanning tree with at most 1 2 (k-1) branch vertices. The third result states that every graph satisfying (*), has a spanning tree with at most 3 2 (k-1) degree sum of branch vertices. All results are sharp.

Publisher:

Изд-во НАН РА

Date created:

2016-11-17

Format:

pdf

Identifier:

oai:arar.sci.am:258885

Location of original object:

ՀՀ ԳԱԱ Հիմնարար գիտական գրադարան