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CONDITIONAL 1

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Treewidth versus clique number. V. Further connections with tree-independence number

math.CO · 2025-05-19 · conditional · novelty 7.0

For complements of line graphs, (tw,omega)-boundedness is equivalent to bounded tree-independence number; (P3+P1)-free graphs have exact tree-independence number equal to their induced biclique number except in one special C5 case; {P4+P1,C4}-free graphs have tree-clique-cover number at most 3.

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  • Treewidth versus clique number. V. Further connections with tree-independence number math.CO · 2025-05-19 · conditional · none · ref 2

    For complements of line graphs, (tw,omega)-boundedness is equivalent to bounded tree-independence number; (P3+P1)-free graphs have exact tree-independence number equal to their induced biclique number except in one special C5 case; {P4+P1,C4}-free graphs have tree-clique-cover number at most 3.