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

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

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 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 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.

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

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 improves the known bounds on the ratio between domination number and packing number in unit disk graphs and bridgeless claw-free cubic graphs.

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 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 constructs a cubic graph with a polyhedral map whose automorphism groups are isomorphic to a given finite group.

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…

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