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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.

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.)
Full Text: DOI
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