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

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 that the average-case complexity of the $k$-coloring problem is $Θ(nk)$ for every $k ≤ n^{c'}$, revealing its average sublinear nature.

The authors prove that the lettericity problem on arbitrary graphs is NP-complete.

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.

Martinsson and Steiner's conjecture on the fractional chromatic number of triangle-free graphs with girth at least 5 is confirmed, and a lower bound is established in a stronger form.

The authors prove that Conformability is NP-complete, settling the complexity of the problem.

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 explores the capabilities and limitations of local search on the vertex coloring problem and introduces a new mutation operator that improves run time.

The paper introduces graph linear notation as an alternative definition for finite graphs, simplifying graph illustration and isomorphism comparison.

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 adapts the distributed triangle-free coloring algorithm of Pettie and Su to solve LLL instances in logarithmic rounds, eliminating the LLL steps as the bottleneck.

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.

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…

The authors extend the one-dimensional lonely set method to two dimensions to study the chromatic number of integer distance graphs in two dimensions.

The authors study the bipanchromatic number χ_B and provide new results and counterexamples to a previous conjecture.

The paper proves that the threshold decision problem for minimizing monochromatic crossing pairs in a graph is NP-complete.