Every graph with treewidth k admits a tree-decomposition of width <=14k+13 with each vertex in <=deg(v)+1 bags, plus a second decomposition of width <=3k-1 with average three bags per vertex.
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2 Pith papers cite this work. Polarity classification is still indexing.
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Every graph of treewidth k and max degree Δ has a tree-partition of width O(kΔ) whose underlying tree has max degree O(Δ) and O(n/kΔ) vertices; domino treewidth is Θ(kΔ²) and a related spread-k bound is tight.
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Tree decompositions with small width, spread, order and degree
Every graph with treewidth k admits a tree-decomposition of width <=14k+13 with each vertex in <=deg(v)+1 bags, plus a second decomposition of width <=3k-1 with average three bags per vertex.
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Tree-partitions and small-spread tree-decompositions
Every graph of treewidth k and max degree Δ has a tree-partition of width O(kΔ) whose underlying tree has max degree O(Δ) and O(n/kΔ) vertices; domino treewidth is Θ(kΔ²) and a related spread-k bound is tight.