Scott–Seymour conjecture on induced odd subdivisions

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For a graph HH, an odd subdivision is a subdivision in which every replacing path has an odd number of edges. Scott–Seymour's conjecture. For every graph HH and integer tt, the class of all graphs with no subgraph isomorphic to Kt,tK_{t,t} and no induced odd subdivision of HH has bounded chromatic number.

This conjecture connects exclusion of complete bipartite subgraphs with induced-subdivision restrictions. The source presents it as an open conjecture combining several themes of the survey.

References

Primary source

Xiying Du and Rose McCarty, “A survey of degree-boundedness”, arXiv:2403.05737 (2024).

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