8 citations · 11 across the 7 of their papers we have counts for
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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…
Simultaneous current graph constructions for minimum triangulations and complete graph embeddings
Timothy Sun
The problems of the genus of the complete graphs and minimum triangulations for each surface were both solved using the theory of current graphs, and each of them divided into twel…
Revisiting Mayer: Symmetric solutions for sporadic cases of the Map Color Theorem
Timothy Sun
The original proof of the genus of the complete graphs depended on Mayer's \emph{ad hoc} solutions for . Recently, an improved solution for was found…
Irregular triangulations of complete graphs on 12s vertices in orientable surfaces
Timothy Sun
We present a family of index 1 abelian current graphs whose derived embeddings can be modified into triangulations of for . Our construction is significantly si…