Connection on differential modules
Constructing and forbidding automorphisms in lifted maps
Constructing regular maps and graphs from planar quotients
Convex 4-valent polytopes with prescribed types of faces
Convex Representations of Maps on the Torus and Other Flat Surfaces.
Counting Lamé differential operators
Crossing numbers and cutwidths.
Crossings, colorings, and cliques.
Curvature on a graph via its geometric spectrum
We approach the problem of defining curvature on a graph by attempting to attach a ‘best-fit polytope’ to each vertex, or more precisely what we refer to as a configured star. How this should be done depends upon the global structure of the graph which is reflected in its geometric spectrum. Mean curvature is the most natural curvature that arises in this context and corresponds to local liftings of the graph into a suitable Euclidean space. We discuss some examples.
Cycle and path embedding on 5-ary N-cubes
We study two topological properties of the 5-ary -cube . Given two arbitrary distinct nodes and in , we prove that there exists an - path of every length ranging from to , where . Based on this result, we prove that is 5-edge-pancyclic by showing that every edge in lies on a cycle of every length ranging from to .
Cycle and Path Embedding on 5-ary N-cubes
We study two topological properties of the 5-ary n-cube . Given two arbitrary distinct nodes x and y in , we prove that there exists an x-y path of every length ranging from 2n to 5n - 1, where n ≥ 2. Based on this result, we prove that is 5-edge-pancyclic by showing that every edge in lies on a cycle of every length ranging from 5 to 5n.
Cycle Double Covers of Infinite Planar Graphs
In this paper, we study the existence of cycle double covers for infinite planar graphs. We show that every infinite locally finite bridgeless k-indivisible graph with a 2-basis admits a cycle double cover.
Cyclic projective planes and Wada dessins.
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.