Decompositions of graphs and hypergraphs into isomorphic factors with a given diameter
Decompositions of Plane Graphs Under Parity Constrains Given by Faces
An edge coloring of a plane graph G is facially proper if no two faceadjacent edges of G receive the same color. A facial (facially proper) parity edge coloring of a plane graph G is an (facially proper) edge coloring with the property that, for each color c and each face f of G, either an odd number of edges incident with f is colored with c, or color c does not occur on the edges of f. In this paper we deal with the following question: For which integers k does there exist a facial (facially proper)...
Decompositions of quadrangle-free planar graphs
W. He et al. showed that a planar graph not containing 4-cycles can be decomposed into a forest and a graph with maximum degree at most 7. This degree restriction was improved to 6 by Borodin et al. We further lower this bound to 5 and show that it cannot be improved to 3.
Delta link-homotopy on spatial graphs.
We study new equivalence relations in spatial graph theory. We consider natural generalizations of delta link-homotopy on links, which is an equivalence relation generated by delta moves on the same component and ambient isotopies. They are stronger than edge-homotopy and vertex-homotopy on spatial graphs which are natural generalizations of link-homotopy on links. Relationship to existing familiar equivalence relations on spatial graphs are stated, and several invariants are defined by using the...
Diagonalizable embedding of composition graphs
Die Klasse der minimalen, nicht-projektiven Graphen mit einer Kreuzhaube.
Die Minimalbasis der Menge aller nicht in die projektive Ebene einbettbaren Graphen.
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.