Supported by NSFC(Grant Nos.12171402,12101600);the Fundamental Research Funds for the Central Universities(Grant Nos.20720190062,2021QN1037)。
In this article we show that any embedded graph has a checkerboard colourable twual,which is equivalent to having a bipartite twual.We also obtain that any Eulerian embedded graph has a checkerboard colourable partial...
Partially supported by NSFC(Grant No.10201002);Partially supported by JSPS(Research No.P03189)
Consider the checkerboard surfaces defined by some link diagrams. When they are not orientable, one considers the boundary surfaces of small regular neighborhoods of them. This article studies the compressibility prob...