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Given a clique-width $k$-expression of a graph $G$, we provide $2^{O(k)}cdot n$ time algorithms for connectivity constraints on locally checkable properties such as Node-Weighted Steiner Tree, Connected Dominating Set, or Connected Vertex Cover. We also propose a $2^{O(k)}cdot n$ time algorithm for Feedback Vertex Set. The best running times for all the considered cases were either $2^{O(kcdot log(k))}cdot n^{O(1)}$ or worse.
Many papers in the field of integer linear programming (ILP, for short) are devoted to problems of the type $max{c^top x colon A x = b,, x in mathbb{Z}^n_{geq 0}}$, where all the entries of $A,b,c$ are integer, parameterized by the number of rows of
We show that there are CNF formulas which can be refuted in resolution in both small space and small width, but for which any small-width proof must have space exceeding by far the linear worst-case upper bound. This significantly strengthens the spa
Seeses conjecture for finite graphs states that monadic second-order logic (MSO) is undecidable on all graph classes of unbounded clique-width. We show that to establish this it would suffice to show that grids of unbounded size can be interpreted in
Butman, Hermelin, Lewenstein, and Rawitz proved that Clique in t-interval graphs is NP-hard for t >= 3. We strengthen this result to show that Clique in 3-track interval graphs is APX-hard.
In analogy with the regularity lemma of Szemeredi, regularity lemmas for polynomials shown by Green and Tao (Contrib. Discrete Math. 2009) and by Kaufman and Lovett (FOCS 2008) modify a given collection of polynomials calF = {P_1,...,P_m} to a new co