3 papers
cs.DS2026
Eulerian-spanning set and coboundary operator: An investigation of maxcut beyond planar graphs
Qiming Fang, Sihong Shao, Yuxuan Wu
Using the concepts of Eulerian-spanning set and coboundary operator, we generalize Hadlock's conversion of the maxcut problem on planar graphs to one on general graphs with non-neg…
math.CO2026
Geometrization of Graphs: Towards Bounding the Chromatic Number via High-Dimensional Embedding
Qiming Fang, Sihong Shao
We establish a geometric framework by transforming a graph into a -dimensional CW complex . This construction is achieved by systematically attaching -sph…
math.CO2025
A High-Dimensional Extension of Wagner's Theorem and the Geometrization of Hypergraphs
Qiming Fang, Sihong Shao
This paper introduces a geometric representation of hypergraphs by representing hyperedges as simplices. Building on this framework, we employ homotopy groups to analyze the topolo…