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@article{1860111, author = {Cooley, Oliver and Garbe, Frederik and Hng, Eng Keat and Kang, Mihyun and SanhuezaandMatamala, Nicolás and Zalla, Julian}, article_number = {4}, doi = {http://dx.doi.org/10.1137/20M1345712}, keywords = {random hypergraphs; paths; phase transition; search algorithm}, language = {eng}, issn = {0895-4801}, journal = {SIAM Journal on Discrete Mathematics}, title = {Longest Paths in Random Hypergraphs}, url = {https://doi.org/10.1137/20M1345712}, volume = {35}, year = {2021} }
TY - JOUR ID - 1860111 AU - Cooley, Oliver - Garbe, Frederik - Hng, Eng Keat - Kang, Mihyun - Sanhueza-Matamala, Nicolás - Zalla, Julian PY - 2021 TI - Longest Paths in Random Hypergraphs JF - SIAM Journal on Discrete Mathematics VL - 35 IS - 4 SP - 2430-2458 EP - 2430-2458 SN - 08954801 KW - random hypergraphs KW - paths KW - phase transition KW - search algorithm UR - https://doi.org/10.1137/20M1345712 N2 - Given integers $k,j$ with $1\le j \le k-1$, we consider the length of the longest $j$-tight path in the binomial random $k$-uniform hypergraph $H^k(n,p)$. We show that this length undergoes a phase transition from logarithmic length to linear and determine the critical threshold, as well as proving upper and lower bounds on the length in the subcritical and supercritical ranges. In particular, for the supercritical case we introduce the \tt Pathfinder algorithm, a depth-first search algorithm which discovers $j$-tight paths in a $k$-uniform hypergraph. We prove that, in the supercritical case, with high probability this algorithm will find a long $j$-tight path. ER -
COOLEY, Oliver, Frederik GARBE, Eng Keat HNG, Mihyun KANG, Nicolás SANHUEZA-MATAMALA and Julian ZALLA. Longest Paths in Random Hypergraphs. \textit{SIAM Journal on Discrete Mathematics}. 2021, vol.~35, No~4, p.~2430-2458. ISSN~0895-4801. Available from: https://dx.doi.org/10.1137/20M1345712.
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