(1,{\lambda})-embedded graphs and the acyclic edge choosability
Combinatorics
2011-12-08 v2 Discrete Mathematics
Abstract
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.
Keywords
Cite
@article{arxiv.1106.4681,
title = {(1,{\lambda})-embedded graphs and the acyclic edge choosability},
author = {Xin Zhang and Guizhen Liu and Jian-Liang Wu},
journal= {arXiv preprint arXiv:1106.4681},
year = {2011}
}
Comments
Please cite this paper as X. Zhang, G. Liu, J.-L. Wu, (1,{\lambda})-embedded graphs and the acyclic edge choosability, Bulletin of the Korean Mathematical Society, to appear