Chromatic Index of Hamiltonian Graphs
Closed retractions of Euclidean spaces
Combinatorial Miller-Morita-Mumford classes and Witten cycles.
Combinatorics of orientation reversing polygons.
Cyclic Crystallizations of Spheres.
Cyclic projective planes and Wada dessins.
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...
Discrete Dirac operators on Riemann surfaces and Kasteleyn matrices
Let be a flat surface of genus with cone type singularities. Given a bipartite graph isoradially embedded in , we define discrete analogs of the Dirac operators on . These discrete objects are then shown to converge to the continuous ones, in some appropriate sense. Finally, we obtain necessary and sufficient conditions on the pair for these discrete Dirac operators to be Kasteleyn matrices of the graph . As a consequence, if these conditions are met, the partition function of the dimer...
Discrete Morse inequalities on infinite graphs.
Discrete Morse theory and graph braid groups.
Dotted links, Heegaard diagrams, and colored graphs for PL 4-manifolds.
The present paper is devoted to establish a connection between the 4-manifold representation method by dotted framed links (or -in the closed case- by Heegaard diagrams) and the so called crystallization theory, which visualizes general PL-manifolds by means of edge-colored graphs.In particular, it is possible to obtain a crystallization of a closed 4-manifold M4 starting from a Heegaard diagram (#m(S1 x S2),ω) and the algorithmicity of the whole process depends on the effective possibility of recognizing...
Double coverings and reflexive abelian hypermaps.
Edge-transitive maps and non-orientable surfaces
Ein verallgemeinerter Gewichtstest mit Anwendungen auf Baumpräsentationen.
Eine Verallgemeinerung der Färbungszahlen. II.
Embeddings of graph braid and surface groups in right-angled Artin groups and braid groups.
Ergodic theory and free actions of groups on IR-trees.
Essential tori admitting a standard tiling
Birman and Menasco (1994) introduced and studied a class of embedded tori in closed braid complements which admit a standard tiling. The geometric description of the tori from this class was not complete. Ng showed (1988) that each essential torus in a closed braid complement which admits a standard tiling possesses a staircase tiling pattern. In this paper, we introduce and study the so-called longitude-meridional patterns for essential tori admitting a standard tiling. A longitude-meridional...
Finite subset spaces of graphs and punctured surfaces.
Fold maps from the sphere to the plane.