1-Planar Graphs
A graph is 1-planar if it can be drawn in the plane so that each edge is crossed at most once. I study optimal 1-planar graphs, analogous drawings on closed surfaces, and related beyond-planar graph classes.
RESEARCH
ResearchResearch Interests
I study graph drawings and structural graph theory on closed surfaces, with a particular focus on 1-planar graphs.
I study optimal 1-planar graphs and related classes from the viewpoints of connectivity, linkedness, matching extendability, and spanning plane subgraphs, with an interest in how geometric restrictions on drawings influence combinatorial structure.
Connectivity & Linkedness
I investigate disjoint paths in highly connected 1-planar graphs, including linkedness in optimal 1-planar graphs and structural characterizations of obstructions.
Matching Extension
I study conditions under which prescribed matchings can be extended to perfect matchings, including problems on closed surfaces and in regular bipartite graphs.
Spanning Plane Subgraphs
I study well-structured spanning plane subgraphs in 1-planar graphs, especially spanning triangulations, their connectivity, and X-mosaics.