Difference metrics for interactive orthogonal graph drawing algorithms.
Dimers and cluster integrable systems
We show that the dimer model on a bipartite graph on a torus gives rise to a quantum integrable system of special type, which we call acluster integrable system. The phase space of the classical system contains, as an open dense subset, the moduli space of line bundles with connections on the graph . The sum of Hamiltonians is essentially the partition function of the dimer model. We say that two such graphs and areequivalentif the Newton polygons of the corresponding partition functions...
Discrete Morse inequalities on infinite graphs.
Disjoint Homotopic Paths and Trees in a Planar Graph.
Dispersed Points and Geometric Embedding of Complete Bipartite Graphs.
Distance in graphs
Distinguishing maps.
Distribution of Points of Odd Degree of Certain Triangulations in the Plane.
Double coverings and reflexive abelian hypermaps.
Drawing 3-polytopes with good vertex resolution.
Drawing a graph in a hypercube.
Drawing clustered graphs on an orthogonal grid.
Drawing graphs on two and three lines.
Drawing planar graphs with large vertices and thick edges.
Dual properties within graph theory
Dynamic WWW structures in .
Edge and vertex operations on upper embeddable graphs
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-disjoint Hamilton cycles in 4-regular planar graphs.
Edge-reconstruction of minimally 3-connected planar graphs.