Shorter Labeling Schemes for Planar Graphs

Bonamy, Marthe; Gavoille, Cyril; Pilipczuk, Michał

doi:10.1137/20m1330464

SIAM J. Discrete Math.

2022

DOI: 10.1137/20m1330464

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Shorter Labeling Schemes for Planar Graphs

Marthe Bonamy¹,

Cyril Gavoille²,

Michał Pilipczuk³

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2024

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Cited by 3 publications

References 39 publications

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Product structure of graphs with an excluded minor

Illingworth,

Scott,

Wood

2024

Trans. Amer. Math. Soc. Ser. B

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This paper shows that K t K_t -minor-free (and K s , t K_{s, t} -minor-free) graphs G G are subgraphs of products of a tree-like graph H H (of bounded treewidth) and a complete graph K m K_m . Our results include optimal bounds on the treewidth of H H and optimal bounds (to within a constant factor) on m m in terms of the number of vertices of G G and the treewidth of G G . These results follow from a more general theorem whose corollaries include a strengthening of the celebrated separator theorem of Alon, Seymour, and Thomas [J. Amer. Math. Soc. 3 (1990), 801–808] and the Planar Graph Product Structure Theorem of Dujmović et al. [J. ACM 67 (2020)].

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Product structure of graphs with an excluded minor

Illingworth,

Scott,

Wood

2024

Trans. Amer. Math. Soc. Ser. B

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Shallow Minors, Graph Products, and Beyond-Planar Graphs

Hickingbotham,

Wood

2024

SIAM J. Discrete Math.

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Small but Unwieldy: A Lower Bound on Adjacency Labels for Small Classes

Bonnet,

Duron,

Sylvester

et al. 2024

SIAM J. Comput.

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Shorter Labeling Schemes for Planar Graphs

Cited by 3 publications

References 39 publications

Product structure of graphs with an excluded minor

Product structure of graphs with an excluded minor

Shallow Minors, Graph Products, and Beyond-Planar Graphs

Small but Unwieldy: A Lower Bound on Adjacency Labels for Small Classes

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