Mixed graph coloring is W[1]-hard parameterized by treewidth and paraNP-hard by neighborhood diversity, but FPT parameterized by the introduced mixed neighborhood diversity.
Easy problems for tree-decomposable graphs
8 Pith papers cite this work. Polarity classification is still indexing.
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Planarizing gadgets do not exist for the recognition problem of (k, l)-tight graphs.
Classifies the classical and parameterized complexity of vertex-identification problems to chordal graph subclasses, with an almost complete picture for parameters k and n-k.
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.
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.
Presents O(nr²) DP algorithms for r-edge and r-facility interdiction covering on trees (and bounded treewidth for the edge version), proves RFIC NP-complete, and gives an O(n³) algorithm for SSBVE on trees.
Maximizing reachability in k-path temporal graphs via budgeted shifts is FPT when parameterized by k and b together or by k alone, but intractable in most other parameterizations with matching XP algorithms.
Model checking for low-monodimensionality fragments of CMSO with disjoint-paths predicate is FPT on topological-minor-free graph classes.
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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.