This paper shows that for every graph, there exist a certain number of vertex-disjoint cycles of different lengths, or a smaller set of vertices such that the graph without these vertices has fewer cy…

This paper presents methods for ranking and unranking permutations avoiding a pattern of length three in lexicographic or colexicographic order.

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

This paper derives multivariate generating functions to refine the enumeration of Fibonacci polyominoes.

The paper resolves three conjectures related to arrow pattern avoidance in permutations using two different proof methods.

This paper presents a set of formulas and equations to compute the longest counting sequence of convex polyominoes of degree of convexity at most 2.

This paper presents an algorithm to generate snake-like polyominoes within a given rectangle and provides exact formulas for the maximal area of such polyominoes for certain dimensions.

The paper establishes bijections between tree records, girth of connected endofunctions, and genesis sequences, deriving generating functions for tree and forest record numbers using Cayley's tree fun…

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

This paper introduces and implements variants of the symmetric lexicographic symmetric-subset reverse search framework for enumerating symmetric feasible subsets of a finite set, applying it to cocirc…

This paper studies the maximum size of an independent set in the discrete simplex graph and provides new bounds using translated smaller graphs and finite rational linear systems.

This paper studies the NP-completeness and provides a polynomial-time algorithm for the disjoint separators problem in planar graphs when all sizes are equal to one.

This paper proves that counting quasi-trees in a connected ribbon graph is #P-complete.

The paper shows that for non-planar orthogonal drawings of a graph, two drawings are sufficient instead of the planar case's three.

The paper explains a method for finding the number of solutions to a system of multivariate polynomial inequalities over a finite field and applies it to find formulas for the number of contiguous sup…

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…