In planar and bounded-genus graphs, absence of k pairwise d-far S-T paths implies a vertex set of size f(d,k) whose d-neighborhood intersects every S-T path.
Thilikos and Sebastian Wiederrecht
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Defines colorful minors on q-colored graphs and proves three structural theorems for H-colorful-minor-free graphs, a q-parameterized Erdős-Pósa classification, and FPT results for testing and colorful-minor-monotone parameters.
Model checking for low-monodimensionality fragments of CMSO with disjoint-paths predicate is FPT on topological-minor-free graph classes.
The paper overviews universal obstructions as a unifying framework for graph parameters, surveys existing results across many parameters, and offers some unifying classification results.
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A coarse Menger's Theorem for planar and bounded genus graphs
In planar and bounded-genus graphs, absence of k pairwise d-far S-T paths implies a vertex set of size f(d,k) whose d-neighborhood intersects every S-T path.
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Colorful Minors
Defines colorful minors on q-colored graphs and proves three structural theorems for H-colorful-minor-free graphs, a q-parameterized Erdős-Pósa classification, and FPT results for testing and colorful-minor-monotone parameters.
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Model Checking for Low Monodimensionality Fragments of CMSO on Topological-Minor-Free Graph Classes
Model checking for low-monodimensionality fragments of CMSO with disjoint-paths predicate is FPT on topological-minor-free graph classes.
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An Overview of Universal Obstructions for Graph Parameters
The paper overviews universal obstructions as a unifying framework for graph parameters, surveys existing results across many parameters, and offers some unifying classification results.