(1,λ)-embedded graphs and the acyclic edge choosability

Details (1,λ)-embedded graphs and the acyclic edge choosability (1,λ)-embedded graphs and the acyclic edge choosability

2011-06-23

arxiv.org/abs/1106.4681v2

Mathematics

Combinatorics

Please cite this paper as X. Zhang, G. Liu, J.-L. Wu, (1,{\lambda})-embedded graphs and the acyclic edge choosability, Bulleti

Scientific paper

A (1,{\lambda})-embedded graph is a graph that can be embedded on a surface with Euler characteristic {\lambda} so that each edge is crossed by at most one other edge. A graph G is called {\alpha}-linear if there exists an integral constant {\beta} such that e(G') \leq {\alpha} v(G')+{\beta} for each G'\subseteq G. In this paper, it is shown that every (1,{\lambda})-embedded graph G is 4-linear for all possible {\lambda}, and is acyclicly edge-(3{\Delta}(G)+70)-choosable for {\lambda}=1,2.

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