Sintiari–Trotignon conjecture on treewidth of diamond-free even-hole-free graphs
Sintiari–Trotignon conjecture on treewidth of diamond-free even-hole-free graphs
For a graph , let denote its treewidth. A graph is even-hole-free if it has no induced cycle of even length at least four, and the diamond is the graph on four vertices with five edges. Sintiari–Trotignon's conjecture. For every integer , there exists a constant such that every even-hole-free graph with no induced diamond and no clique of size satisfies
This conjecture was resolved in the cited work TWXI, so the asserted bounded-treewidth conclusion is now a theorem.
Sources & referencesView supporting material
Primary source
Maria Chudnovsky, Peter Gartland, Sepehr Hajebi, Daniel Lokshtanov and Sophie Spirkl, “Induced subgraphs and tree decompositions XV. Even-hole-free graphs with bounded clique number have logarithmic treewidth”, arXiv:2402.14211 (2024).
Additional references
2 papers in this index state this conjecture (2022–2024). The statement above is taken from the most recent of them; the others are arXiv:2203.06775.
Progress summary
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