Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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(1,λ)-EMBEDDED GRAPHS AND THE ACYCLIC EDGE CHOOSABILITY

  • Received : 2011.01.31
  • Published : 2012.05.31
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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 $e(G^{\prime}){\leq}{\alpha}v(G^{\prime})+{\beta}$ for each $G^{\prime}{\subseteq}G$. 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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References

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