8 citations · 21 across the 14 of their papers we have counts for
15 papers
Settling the nonorientable genus of the nearly complete bipartite graphs
Warren Singh, Timothy Sun
A graph is said to be nearly complete bipartite if it can be obtained by deleting a set of independent edges from a complete bipartite graph. The nonorientable genus of such graphs…
Face-simple minimal quadrangulations of surfaces
Sarah Abusaif, Warren Singh, Timothy Sun
For each surface besides the sphere, projective plane, and Klein bottle, we construct a face-simple minimal quadrangulation, i.e., a simple quadrangulation on the fewest number of…
Index 3 biembeddings of the complete graphs
Juvenal F. Barajas, Timothy Sun
We show that the complete graphs on vertices have decompositions into two edge-disjoint subgraphs, each of which triangulates an orientable surface. The special case where…
On the bigenus of the complete graphs
Timothy Sun
We describe an infinite family of edge-decompositions of complete graphs into two graphs, each of which triangulate the same orientable surface. Previously, such decompositions had…
Settling the genus of the -prism
Timothy Sun
In a 1977 paper, Ringel conjectured a formula for the genus of the -prism and verified its correctness for about five-sixths of all values . We complete this…
Jungerman ladders and index 2 constructions for genus embeddings of dense regular graphs
Timothy Sun
We construct several families of minimum genus embeddings of dense graphs using index 2 current graphs. In particular, we complete the genus formula for the octahedral graphs, solv…