MSO transduction recovers the laminar tree from a laminar set system, resolving Courcelle's question and enabling MSO constructions for modular, split, and bi-join decompositions.
Makowsky, and Udi Rotics
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Full complexity classification for three b- and fall-coloring problems in H-free graphs plus a separation showing b-Chromatic Number can be NP-hard while Tight b-Chromatic Number is P-time solvable for some H.
Fair MSO1 problems are W[1]-hard parameterized by cluster vertex deletion in general, but admit FPT algorithms under a sufficient condition that includes fair feedback vertex set, vertex cover, dominating set, and odd cycle transversal.
The paper overviews universal obstructions as a unifying framework for graph parameters, surveys existing results across many parameters, and offers some unifying classification results.
citing papers explorer
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The role of counting quantifiers in laminar set systems
MSO transduction recovers the laminar tree from a laminar set system, resolving Courcelle's question and enabling MSO constructions for modular, split, and bi-join decompositions.
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Optimal b-Colourings and Fall Colourings in $H$-Free Graphs
Full complexity classification for three b- and fall-coloring problems in H-free graphs plus a separation showing b-Chromatic Number can be NP-hard while Tight b-Chromatic Number is P-time solvable for some H.
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Fair Vertex Problems Parameterized by Cluster Vertex Deletion
Fair MSO1 problems are W[1]-hard parameterized by cluster vertex deletion in general, but admit FPT algorithms under a sufficient condition that includes fair feedback vertex set, vertex cover, dominating set, and odd cycle transversal.
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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.