Maximum Edge Colouring Problem On Graphs That Exclude a Fixed Minor

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F23%3A10473814" target="_blank" >RIV/00216208:11320/23:10473814 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1007/978-3-031-43380-1_21" target="_blank" >https://doi.org/10.1007/978-3-031-43380-1_21</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/978-3-031-43380-1_21" target="_blank" >10.1007/978-3-031-43380-1_21</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Maximum Edge Colouring Problem On Graphs That Exclude a Fixed Minor

Popis výsledku v původním jazyce

The maximum edge colouring problem considers the maximum colour assignment to edges of a graph under the condition that every vertex has at most a fixed number of distinct coloured edges incident on it. If that fixed number is q we call the colouring a maximum edge q-colouring. The problem models a non-overlapping frequency channel assignment question on wireless networks. The problem has also been studied from a purely combinatorial perspective in the graph theory literature. We study the question when the input graph is sparse. We show the problem remains NP-hard on 1-apex graphs. We also show that there exists PTAS for the problem on minor-free graphs. The PTAS is based on a recently developed Baker game technique for proper minor-closed classes, thus avoiding the need to use any involved structural results. This further pushes the Baker game technique beyond the problems expressible in the first-order logic.

Název v anglickém jazyce

Maximum Edge Colouring Problem On Graphs That Exclude a Fixed Minor

Popis výsledku anglicky

The maximum edge colouring problem considers the maximum colour assignment to edges of a graph under the condition that every vertex has at most a fixed number of distinct coloured edges incident on it. If that fixed number is q we call the colouring a maximum edge q-colouring. The problem models a non-overlapping frequency channel assignment question on wireless networks. The problem has also been studied from a purely combinatorial perspective in the graph theory literature. We study the question when the input graph is sparse. We show the problem remains NP-hard on 1-apex graphs. We also show that there exists PTAS for the problem on minor-free graphs. The PTAS is based on a recently developed Baker game technique for proper minor-closed classes, thus avoiding the need to use any involved structural results. This further pushes the Baker game technique beyond the problems expressible in the first-order logic.

Druh

D - Stať ve sborníku

CEP obor

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OECD FORD obor

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

Projekt

<a href="/cs/project/GA22-17398S" target="_blank" >GA22-17398S: Toky a cykly v grafech na plochách</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2023

Kód důvěrnosti údajů

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

Název statě ve sborníku

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

ISBN

978-3-031-43379-5

ISSN

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e-ISSN

1611-3349

Počet stran výsledku

14

Strana od-do

291-304

Název nakladatele

Springer

Místo vydání

Switzerland

Místo konání akce

Fribourg, Switzerland

Datum konání akce

28. 6. 2023

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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