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math.CO2022
The average Euler-genus of the vertex-amalgamation of signed graphs
Yichao Chen
In this paper, we first generalize a theorem for counting the number of faces of an oriented embedding of a graph that passing through a given cut-edge set [S. Stahl, Trans. Amer.…
math.CO2022
Permutation-bipartition pairs
Yichao Chen
Permutation-partition pairs were introduced by Stahl in 1980. These pairs are generalizations of graphs and graphs on surfaces. They were used to solve some problems for orientable…
math.CO2022
Partial-duals for planar ribbon graphs
Qiyao Chen, Yichao Chen
In 2009, Chmutov introduced the partial-duality for a ribbon graph . Recently, Gross, Mansour and Tucker enumerated all possible partial-duals of by genus and introduced the…