The paper introduces and explores Truly Linear FPT (TLFPT), a complexity class defined by $O(n) + f(k)$, demonstrating that it is a strict subset of standard Linear FPT and providing new algorithms fo…

The paper removes stability requirement from the progressive exploration algorithm for Dominating Set, yielding a fixed-parameter tractable algorithm on certain graph classes.

This paper studies the computational complexity of Maximum Edge Open Packing Problem in distance-hereditary, biconvex bipartite, and chordal graphs, providing polynomial-time algorithms and a fixed-pa…

This paper shows #P-completeness for several graph counting problems using a new technique.

This paper provides bounds on the neighborhood complexity of graphs with bounded treewidth and pathwidth, and constructs reaching these bounds.

This paper shows that finding the minimum geodetic set in chordal graphs is fixed parameter tractable, implying a polynomial-time algorithm for k-trees. It also proves that the problem is NP-hard on i…

The paper introduces a method to efficiently detect 'essential' constraints in Boolean MinCSPs, significantly reducing the search space for solving these problems and providing a dichotomy theorem for…

KoAT is a tool that automatically infers complexity bounds and proves termination of integer programs using an alternating modular analysis approach and a portfolio of techniques.

This paper studies the decidability and complexity properties of unary three-way and two-way deterministic and nondeterministic two-dimensional automata.

This paper proves that the minimum edge-outerplanarity of a planar graph can be computed in polynomial time.

This paper studies the structural expressivity and parameterized complexity of counting homomorphisms from small temporal patterns to large temporal graphs, proving a temporal Lovász-style theorem, in…

The paper shows that every problem asking if a given graph has an edge-coloring without an edge-colored clique from a fixed family is poly-time equivalent to a Constraint Satisfaction Problem, resulti…

This paper proves a new lower bound of $ ildeΩ(n^2)$ for read-once parity branching programs on boolean functions, improving upon the previous bound of $ ildeΩ(n^{1.5})$.

This paper connects a generalized notion of tensor rank with multiplicative complexity, enabling control of arithmetic complexity in any constant degree of multilinearity and applications to fine-grai…

This paper presents approximation algorithms for the one-way directed Reachability-Preserving Minimum Edge Cut problem in directed graphs.

This paper introduces structured cut sets, a novel preprocessing technique for Maximum k-Cut, and extends existing techniques from Maximum Cut. The rules are optimality-preserving and yield significan…

A new polynomial-time algorithm is presented for optimally coloring perfect graphs using graph-theoretic operations and iterative walk counting.