Graph Product Structure for h-Framed Graphs

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F22%3A00129307" target="_blank" >RIV/00216224:14330/22:00129307 - isvavai.cz</a>

Result on the web

<a href="https://doi.org/10.4230/LIPIcs.ISAAC.2022.23" target="_blank" >https://doi.org/10.4230/LIPIcs.ISAAC.2022.23</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4230/LIPIcs.ISAAC.2022.23" target="_blank" >10.4230/LIPIcs.ISAAC.2022.23</a>

Result language

angličtina

Original language name

Graph Product Structure for h-Framed Graphs

Original language description

Graph product structure theory expresses certain graphs as subgraphs of the strong product of much simpler graphs. In particular, an elegant formulation for the corresponding structural theorems involves the strong product of a path and of a bounded treewidth graph, and allows to lift combinatorial results for bounded treewidth graphs to graph classes for which the product structure holds, such as to planar graphs [Dujmović et al., J. ACM, 67(4), 22:1-38, 2020]. In this paper, we join the search for extensions of this powerful tool beyond planarity by considering the h-framed graphs, a graph class that includes 1-planar, optimal 2-planar, and k-map graphs (for appropriate values of h). We establish a graph product structure theorem for h-framed graphs stating that the graphs in this class are subgraphs of the strong product of a path, of a planar graph of treewidth at most 3, and of a clique of size 3⌊ h/2 ⌋+⌊ h/3 ⌋-1. This allows us to improve over the previous structural theorems for 1-planar and k-map graphs. Our results constitute significant progress over the previous bounds on the queue number, non-repetitive chromatic number, and p-centered chromatic number of these graph classes, e.g., we lower the currently best upper bound on the queue number of 1-planar graphs and k-map graphs from 115 to 82 and from ⌊ 33/2(k+3 ⌊ k/2⌋ -3)⌋ to ⌊ 33/2 (3⌊ k/2 ⌋+⌊ k/3 ⌋-1) ⌋, respectively. We also employ the product structure machinery to improve the current upper bounds on the twin-width of 1-planar graphs from O(1) to 80. All our structural results are constructive and yield efficient algorithms to obtain the corresponding decompositions.

Czech name

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Czech description

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Type

D - Article in proceedings

CEP classification

—

OECD FORD branch

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

Project

<a href="/en/project/GA20-04567S" target="_blank" >GA20-04567S: Structure of tractable instances of hard algorithmic problems on graphs</a><br>

Continuities

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

Publication year

2022

Confidentiality

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

Article name in the collection

33rd International Symposium on Algorithms and Computation (ISAAC 2022)

ISBN

9783959772587

ISSN

1868-8969

e-ISSN

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Number of pages

15

Pages from-to

„23:1“-„23:15“

Publisher name

Schloss Dagstuhl

Place of publication

Dagstuhl, Germany

Event location

Seoul, Korea

Event date

Dec 19, 2022

Type of event by nationality

WRD - Celosvětová akce

UT code for WoS article

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