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

The paper shows that an oddomorphism between graphs does not imply graph minor containment and introduces a new structural relation called split-off minor.

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

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

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

This paper proves DP-completeness of Exact-3-DNP and Exact-4-DNP by reducing 3SAT to these problems.

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