This paper studies the problem of finding totally disjoint diametral paths in simple connected graphs and provides algorithms for certain classes of graphs.

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

The paper simplifies and speeds up an algorithm for computing a Hamilton path on the skeleton of a 0/1-polytope by removing the log n factor, leading to improved algorithms for various problems.

This paper improves the time complexity of exact algorithms for converting a connected graph into a cactus by reducing it from O*(3^n) to O*(2^n) for unweighted graphs, and provides faster algorithms…

This paper disproves a conjecture about the longest-path lengths of MaxSTN and MinSTN algorithms for producing $st$-orientations of biconnected graphs.

The authors map the problem of finding the maximum cut of a planar graph with arbitrary weights to a minimum T-join problem in the absolute dual graph, enabling the use of shortest paths and adapting…

The paper proves XNLP-hardness of Directed Edge Geography and Undirected Edge Geography when parameterized by pathwidth, and shows their fixed-parameter tractability when parameterized by treewidth an…

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

This paper provides new upper bounds and algorithms for the shortest path map equivalence decomposition of a polygonal domain, leading to solutions for two-point shortest path queries, geodesic diamet…

The paper formalizes Razborov's flag algebra method for finite simple graphs and creates a compiler to transform certificate data into algebraic proofs checked by Lean.

This paper settles the complexity of three sketching problems in graphs and distributions.

This paper investigates the complexity of recognizing domatically critical graphs, which are graphs with maximum dominating sets that cannot be increased by deleting any edge.

This paper introduces a new variant of the Traveling Salesman Problem where the goal is to find two paths connecting a set of sites while minimizing the Fréchet distance between the two paths.

This paper presents an optimized algorithm for computing cut sets of a path set in graph theory and introduces a vectorized computational framework for property calculations.

This paper identifies a tractability island inside the contextual-fraction problem by collapsing it to a fixed-point calculation for a specific class of permutation-transport models.

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