Graphs with independence number ≤2 and no strong odd Kt-immersion satisfy χ(G) ≤ ⌈3(t-1)/2⌉.
Zang,Proof of Toft’s Conjecture: Every Graph Containing No Fully OddK 4 is 3-Colorable
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Coloring graphs with independence number two and no odd clique immersions
Graphs with independence number ≤2 and no strong odd Kt-immersion satisfy χ(G) ≤ ⌈3(t-1)/2⌉.