(1,λ)-EMBEDDED GRAPHS AND THE ACYCLIC EDGE CHOOSABILITY

Title & Authors
(1,λ)-EMBEDDED GRAPHS AND THE ACYCLIC EDGE CHOOSABILITY
Zhang, Xin; Liu, Guizhen; Wu, Jian-Liang;

Abstract
A (1, $\small{{\lambda}}$)-embedded graph is a graph that can be embedded on a surface with Euler characteristic $\small{{\lambda}}$ so that each edge is crossed by at most one other edge. A graph $\small{G}$ is called $\small{{\alpha}}$-linear if there exists an integral constant $\small{{\beta}}$ such that $\small{e(G^{\prime}){\leq}{\alpha}v(G^{\prime})+{\beta}}$ for each $\small{G^{\prime}{\subseteq}G}$. In this paper, it is shown that every (1, $\small{{\lambda}}$)-embedded graph $\small{G}$ is 4-linear for all possible $\small{{\lambda}}$, and is acyclicly edge-($\small{3{\Delta}(G)+70}$)-choosable for $\small{{\lambda}}$
Keywords
(1, $\small{{\lambda}}$)-embedded graph;$\small{{\alpha}}$-linear graph;acyclic edge choosability;
Language
English
Cited by
1.
On edge colorings of 1-toroidal graphs, Acta Mathematica Sinica, English Series, 2013, 29, 7, 1421
2.
On total colorings of 1-planar graphs, Journal of Combinatorial Optimization, 2015, 30, 1, 160
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