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Graph minors and metric spaces

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arxiv 2305.07456 v3 pith:WUY5GWMK submitted 2023-05-12 math.CO math.GTmath.MG

Agelos Georgakopoulos , Panos Papasoglu This is my paper · ORCID
classification math.COmath.GTmath.MG
keywords graphmetrictheoremminoraffirmativelyanalogueanaloguesanswer
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abstract

We present problems and results that combine graph-minors and coarse geometry. For example, we ask whether every geodesic metric space (or graph) without a fat $H$ minor is quasi-isometric to a graph with no $H$ minor, for an arbitrary finite graph $H$. We answer this affirmatively for a few small $H$. We also present a metric analogue of Menger's theorem and Konig's ray theorem. We conjecture metric analogues of the Erdos--Posa Theorem and Halin's grid theorem.

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Cited by 7 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Asymptotic structure. III. Excluding a fat tree

    math.CO 2025-09 conditional novelty 8.0 of 10

    Any graph lacking a c-fat tree minor can be quasi-isometrically approximated by a graph with line-width bounded in terms of the tree and c.

  2. Asymptotic structure. V. The coarse Menger conjecture in bounded path-width

    math.CO 2025-09 conditional novelty 8.0 of 10

    The coarse Menger conjecture is true for all graphs of bounded path-width.

  3. A coarse Halin Grid Theorem with applications to quasi-transitive, locally finite graphs

    math.CO 2025-07 conditional novelty 8.0 of 10

    A one-ended locally finite graph has the half-grid as an asymptotic minor whenever it has the disjoint union of rays as an asymptotic minor; every one-ended quasi-transitive locally finite graph contains an ultra-fat ...

  4. Asymptotic structure. VI. Distant paths across a disc

    math.CO 2025-09 conditional novelty 7.0 of 10

    For planar graphs with all terminals on the outer face, the coarse Menger conjecture holds: either k+1 pairwise far paths exist, or k small connected subgraphs of bounded total diameter block all paths.

  5. Coarse Balanced Separators and Tree-Decompositions

    math.CO 2025-05 conditional novelty 7.0 of 10

    For K_{t,t}-free graphs, bounded coarse balanced separators with radius 1 imply a (k',2)-centred tree-decomposition, hence bounded coarse treewidth.

  6. Tree independence number V. Walls and claws

    math.CO 2025-01 conditional novelty 7.0 of 10

    For every fixed t, L_t ∪ {S_t,t,t,K_t,t}-free n-vertex graphs have tree independence number O(log^4 n).

  7. Graph parameters that are coarsely equivalent to tree-length

    math.CO 2025-02 accept novelty 6.0 of 10

    Tree-length is within constant factors of bramble interception radius, Helly-family interception radius, same-vertex-set additive tree distortion, and two new cycle bridging parameters.

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