-locally connected graphs and their upper embeddability
Navigating clustered graphs using force-directed methods.
Near-homogeneous spherical Latin bitrades
A planar Eulerian triangulation is a simple plane graph in which each face is a triangle and each vertex has even degree. Such objects are known to be equivalent to spherical Latin bitrades. (A Latin bitrade describes the difference between two Latin squares of the same order.) We give a classification in the near-regular case when each vertex is of degree or (which we call a near-homogeneous spherical Latin bitrade, or NHSLB). The classification demonstrates that any NHSLB is equal to two graphs...
Neighbor sum distinguishing list total coloring of IC-planar graphs without 5-cycles
Let be a simple graph and denote the set of edges incident with a vertex . A neighbor sum distinguishing (NSD) total coloring of is a proper total coloring of such that for each edge . Pilśniak and Woźniak asserted in 2015 that each graph with maximum degree admits an NSD total -coloring. We prove that the list version of this conjecture holds for any IC-planar graph with but without -cycles by applying the Combinatorial Nullstellensatz.
Neighborly Maps with Few Vertices.
New infinite families of almost-planar crossing-critical graphs.
New lower bounds for orthogonal drawings.
New upper bounds for the crossing number of on the Klein bottle
Non-orientable biembeddings of Steiner triple systems of order 15.
Nonorientable Genus of Nearly Complete Bipartite Graphs.
Note on Induced Subgraphs of the Unit Distance Graph En.
Note on the weight of paths in plane triangulations of minimum degree 4 and 5
The weight of a path in a graph is defined to be the sum of degrees of its vertices in entire graph. It is proved that each plane triangulation of minimum degree 5 contains a path P₅ on 5 vertices of weight at most 29, the bound being precise, and each plane triangulation of minimum degree 4 contains a path P₄ on 4 vertices of weight at most 31.