On the Structure of Hamiltonian Graphs with Small Independence Number
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F24%3A10493336" target="_blank" >RIV/00216208:11320/24:10493336 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/978-3-031-63021-7_14" target="_blank" >https://doi.org/10.1007/978-3-031-63021-7_14</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-3-031-63021-7_14" target="_blank" >10.1007/978-3-031-63021-7_14</a>
Alternative languages
Result language
angličtina
Original language name
On the Structure of Hamiltonian Graphs with Small Independence Number
Original language description
A Hamiltonian path (cycle) in a graph is a path (cycle, respectively) which passes through all of its vertices. The problems of deciding the existence of a Hamiltonian cycle (path) in an input graph are well known to be NP-complete, and restricted classes of graphs which allow for their polynomial-time solutions are intensively investigated. Until very recently the complexity was open even for graphs of independence number at most 3. A so far unpublished result of Jedlickova and Kratochvil [arXiv:2309.09228] shows that for every integer k, the problems of deciding the existence of a Hamiltonian path and cycle are polynomial-time solvable in graphs of independence number bounded by k. As a companion structural result, in this paper, we determine explicit obstacles for the existence of a Hamiltonian path for small values of k, namely for graphs of independence number 2, 3, and 4. Identifying these obstacles in an input graph yields alternative polynomial-time algorithms for deciding the existence of a Hamiltonian path with no large hidden multiplicative constants.
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
CEP classification
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Result continuities
Project
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Continuities
S - Specificky vyzkum na vysokych skolach<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
COMBINATORIAL ALGORITHMS, IWOCA 2024
ISBN
978-3-031-63020-0
ISSN
0302-9743
e-ISSN
1611-3349
Number of pages
13
Pages from-to
180-192
Publisher name
SPRINGER INTERNATIONAL PUBLISHING AG
Place of publication
CHAM
Event location
Ischia
Event date
Jul 1, 2024
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
001282050500014