Polynomial kernels exist for Leaf & Internal-Constrained Diverse Spanning Trees (parameter p+q+k+ℓ) and Leaf & Non-terminal-Constrained Diverse Spanning Trees (parameter p+|V_NT|+k+ℓ).
Downey and Michael R
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Defines TLFPT as O(n) + f(k) algorithms, proves it is strictly contained in Linear FPT via diagonalization, and exhibits several problems (SAT, Vertex Cover, k-Path, etc.) that belong to TLFPT under parameters such as treedepth and BFS-width.
citing papers explorer
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Polynomial Kernels for Spanning Tree with Diversity Requirements
Polynomial kernels exist for Leaf & Internal-Constrained Diverse Spanning Trees (parameter p+q+k+ℓ) and Leaf & Non-terminal-Constrained Diverse Spanning Trees (parameter p+|V_NT|+k+ℓ).
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$O(n +f(k))$: Truly Linear FPT
Defines TLFPT as O(n) + f(k) algorithms, proves it is strictly contained in Linear FPT via diagonalization, and exhibits several problems (SAT, Vertex Cover, k-Path, etc.) that belong to TLFPT under parameters such as treedepth and BFS-width.