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.
Seymour, and Robin Thomas
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A decomposition-based framework finds entire sets of irrelevant vertices in linear time on bounded-genus graphs, enabling linear-time algorithms for minor containment, disjoint paths, and deletion problems.
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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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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Finding irrelevant vertices in linear time on bounded-genus graphs
A decomposition-based framework finds entire sets of irrelevant vertices in linear time on bounded-genus graphs, enabling linear-time algorithms for minor containment, disjoint paths, and deletion problems.
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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.