(1,{\lambda})-embedded graphs and the acyclic edge choosability

  title={(1,\{\lambda\})-embedded graphs and the acyclic edge choosability},
  author={Xin Zhang and Guizhen Liu and Jian-Liang Wu},
A (1, λ)-embedded graph is a graph that can be embedded on a surface with Euler characteristic λ so that each edge is crossed by at most one other edge. A graph G is called α-linear if there exists an integral constant β such that e(G′) ≤ αv(G′) + β for each G′ ⊆ G. In this paper, it is shown that every (1, λ)-embedded graph G is 4-linear for all possible λ, and is acyclicly edge-(3∆(G) + 70)-choosable for λ = 1, 2.