Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)


For citation:

Osipov D. Y. T-irreducible Extensions for Starlike Trees. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2015, vol. 15, iss. 3, pp. 330-339. DOI: 10.18500/1816-9791-2015-15-3-330-339, EDN: UKIVHD

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
11.09.2015
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Russian
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UDC: 
519.17
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UKIVHD

T-irreducible Extensions for Starlike Trees

Autors: 
Osipov Dmitrii Yur'evich, Saratov State University
Abstract: 

We deal with a sort of optimal extensions of graphs, so called T-irreducible extensions. T-irreducible extension of a graph G is an extension of G obtained by removing a maximal set of edges from the trivial extension of G. A difficult starlike tree is a starlike tree that has at least one difficult node. T-irreducible extensions for nondifficult starlike trees were constructed by M. B. Abrosimov, T-irreducible extensions for palms (one of subclasses of starlike trees) were constructed by S. G. Kurnosova. Counterexamples were found to a method of Harary and Khurum, who tried to construct possible T-irreducible extensions for starlike trees. T-irreducible extensions for difficult starlike trees are constructed.

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Received: 
25.04.2015
Accepted: 
27.08.2015
Published: 
30.09.2015