On 2-walks in chordal planar graphs

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F05%3A00000223" target="_blank" >RIV/49777513:23520/05:00000223 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
On 2-walks in chordal planar graphs
Original language description
A 2-walk is a closed spanning trail which uses every vertex at most twice. A graph is said to be chordal if each cycle different from 3-cycle has a chord. The toughness of a non-complete graph is t(G) = min( |S| c(G-S) ), where the minimum is taken overall nonempty vertex sets S, for which c(G-S) >1 and c(G-S) denotes the number of components of the graph G-S. We prove that every chordal planar graph G with toughness t(G) > 3/4 has a 2-walk. Then we show the existence of an in¯nite class of 2-connected chordal planar graphs with toughness 1 2 and without a 2-walk, followed by conjectures and open problems.
Czech name
On 2-walks in chordal planar graphs
Czech description
A 2-walk is a closed spanning trail which uses every vertex at most twice. A graph is said to be chordal if each cycle different from 3-cycle has a chord. The toughness of a non-complete graph is t(G) = min( |S| c(G-S) ), where the minimum is taken overall nonempty vertex sets S, for which c(G-S) >1 and c(G-S) denotes the number of components of the graph G-S. We prove that every chordal planar graph G with toughness t(G) > 3/4 has a 2-walk. Then we show the existence of an in¯nite class of 2-connected chordal planar graphs with toughness 1 2 and without a 2-walk, followed by conjectures and open problems.

Project
<a href="/en/project/1M0545" target="_blank" >1M0545: Institute for Theoretical Computer Science</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2005
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection
Proceedings of the Sixteenth Australasian Workshop on Combinatorial Algorithms
ISBN
0-646-45252-5
ISSN
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e-ISSN
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Number of pages
8
Pages from-to
333-340
Publisher name
University of Ballarat
Place of publication
Ballarat
Event location
Ballarat, Victoria, Australia
Event date
Jan 1, 2005
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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