Graph Product Structure for h-Framed Graphs
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F24%3A00139110" target="_blank" >RIV/00216224:14330/24:00139110 - isvavai.cz</a>
Result on the web
<a href="https://www.combinatorics.org/ojs/index.php/eljc/article/view/v31i4p56" target="_blank" >https://www.combinatorics.org/ojs/index.php/eljc/article/view/v31i4p56</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.37236/12123" target="_blank" >10.37236/12123</a>
Alternative languages
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 lead to 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 72. 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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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Result continuities
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)<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
Name of the periodical
ELECTRONIC JOURNAL OF COMBINATORICS
ISSN
1077-8926
e-ISSN
1077-8926
Volume of the periodical
31
Issue of the periodical within the volume
4
Country of publishing house
US - UNITED STATES
Number of pages
33
Pages from-to
„P4.56“
UT code for WoS article
001367413400001
EID of the result in the Scopus database
2-s2.0-85211233237