The authors improve the bound on the chromatic number of t-perfect graphs from 199053 to 186 by refining the proof of Chudnovsky et al.

This paper uses local flag algebra to prove bounds on the strong chromatic index of graphs, making progress towards established conjectures for general, bipartite, and asymmetric bipartite graphs.

This paper studies set-defined graph classes and proves that bounded unions of shift-colorable graphs form the fundamental obstruction to chromatic number boundness in these classes.

This paper studies the complexity of the graph homomorphism problem in terms of the degeneracy of the target graph and shows that under ETH, there is no efficient algorithm for this problem.

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

This paper shows that for a digraph with large maximum product of in- and out-degrees, either there exists a large biclique or the dichromatic number is smaller than expected.

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

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 proves that every simple planar graph with no copy of C8 has at most 69/25(n-2) edges, improving the previous bound.

This paper provides bounds on the difference between the annihilation number and independence number of a finite simple graph, and proves these bounds for various types of graphs.

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

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 studies the complexity of the Flood-It game on various graph classes and provides polynomial-time algorithms for Free Flood-It on graphs free of certain jewels, while proving NP-completenes…

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

This paper provides a bound on the hat guessing number of a graph based on its order and maximum degree.

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

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…