Edge-bandwidth of the triangular grid.
Edge-choosability and total-choosability of planar graphs with no adjacent 3-cycles
Let G be a planar graph with no two 3-cycles sharing an edge. We show that if Δ(G) ≥ 9, then χ'ₗ(G) = Δ(G) and χ''ₗ(G) = Δ(G)+1. We also show that if Δ(G) ≥ 6, then χ'ₗ(G) ≤ Δ(G)+1 and if Δ(G) ≥ 7, then χ''ₗ(G) ≤ Δ(G)+2. All of these results extend to graphs in the projective plane and when Δ(G) ≥ 7 the results also extend to graphs in the torus and Klein bottle. This second edge-choosability result improves on work of Wang and Lih and of Zhang and Wu. All of our results use the discharging method...
Edge-magic group labellings of countable graphs.
Edge-sum distinguishing labeling
We study edge-sum distinguishing labeling, a type of labeling recently introduced by Z. Tuza (2017) in context of labeling games. An ESD labeling of an -vertex graph is an injective mapping of integers to to its vertices such that for every edge, the sum of the integers on its endpoints is unique. If equals to , we speak about a canonical ESD labeling. We focus primarily on structural properties of this labeling and show for several classes of graphs if they have or do not have a canonical...
Efficient counting and asymptotics of -noncrossing tangled diagrams.
Explicit Ramsey graphs and orthonormal labelings.
Extension of -labelings of quadratic graphs.