Gould, Horn and Magnant's chorded-cycle packing conjecture

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Let c,kc,k be integers with c≥2c\geq 2 and k≥1k\geq 1. For an integer r≥0r\geq 0, an rr-chorded cycle is a cycle with rr chords. Gould, Horn and Magnant's conjecture. Every graph GG of order at least (c+1)k(c+1)k with minimum degree δ(G)≥ck\delta(G)\geq ck contains kk vertex-disjoint (c+1)(c−2)2\frac{(c+1)(c-2)}{2}-chorded cycles.

This conjecture is presented as a common generalization of Corrádi–Hajnal's theorem on disjoint cycles and Hajnal–Szemerédi's theorem on disjoint complete graphs. Its resolution is not specified in the source.

References

Primary source

Shuya Chiba and Nicolas Lichiardopol, “On the existence of vertex-disjoint subgraphs with high degree sum”, arXiv:1503.03272 (2017).

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