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Every triangle-free induced subgraph of the triangular lattice is $$(5m,2m)$$-choosable. (English) Zbl 1283.05182
Summary: A graph $$G$$ is $$(a,b)$$-choosable if for any color list of size $$a$$ associated with each vertex, one can choose a subset of $$b$$ colors such that adjacent vertices are colored with disjoint color sets. This paper proves that for any integer $$m\geq 1$$, every finite triangle-free induced subgraph of the triangular lattice is $$(5m,2m)$$-choosable.

##### MSC:
 05C60 Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.) 05C22 Signed and weighted graphs 94A12 Signal theory (characterization, reconstruction, filtering, etc.)
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