On the Structure of Hamiltonian Graphs with Small Independence Number

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

On the Structure of Hamiltonian Graphs with Small Independence Number

Popis výsledku v původním jazyce

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 A so far unpublished result of Jedlickova and Kratochvil [arXiv:2309.09228] shows that for every integer k, the problems of deciding the existence of a Hamiltonian path and cycle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.

Název v anglickém jazyce

On the Structure of Hamiltonian Graphs with Small Independence Number

Popis výsledku anglicky

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 A so far unpublished result of Jedlickova and Kratochvil [arXiv:2309.09228] shows that for every integer k, the problems of deciding the existence of a Hamiltonian path and cycle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.

Druh

D - Stať ve sborníku

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2024

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

COMBINATORIAL ALGORITHMS, IWOCA 2024

ISBN

978-3-031-63020-0

ISSN

0302-9743

e-ISSN

1611-3349

Počet stran výsledku

13

Strana od-do

180-192

Název nakladatele

SPRINGER INTERNATIONAL PUBLISHING AG

Místo vydání

CHAM

Místo konání akce

Ischia

Datum konání akce

1. 7. 2024

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

001282050500014