TY - JOUR
T1 - A Note on Color-Bias Perfect Matchings in Hypergraphs
AU - Balogh, József
AU - Treglown, Andrew
AU - Zárate-Guerén, Camila
N1 - Acknowledgments. Part of this research was carried out during a visit by the first author to the University of Birmingham in July 2023. The authors are grateful to the BRIDGE strategic alliance between the University of Birmingham and the University of Illinois at Urbana-Champaign, which partially funded this visit. The authors are also grateful to the referees for their careful reviews.
\\ast Received by the editors February 6, 2024; accepted for publication (in revised form) July 8, 2024; published electronically October 4, 2024. https://doi.org/10.1137/24M1637350 Funding: The first author's research was supported in part by NSF grants DMS-1764123, RTG DMS-1937241, and FRG DMS-2152488; by the Arnold O. Beckman Research Award (UIUC Campus Research Board RB 24012)' and by the Langan Scholar Fund (UIUC). The second author's research was supported by EPSRC grant EP/V002279/1. The third author's research was supported by EPSRC. \\dagger Department of Mathematics, University of Illinois Urbana-Champaign, Urbana, IL 61801 USA ([email protected]). \\ddagger School of Mathematics, University of Birmingham, Birmingham, UK ([email protected], [email protected]).
PY - 2024
Y1 - 2024
N2 - A result of Balogh et al. yields the minimum degree threshold that ensures a 2- colored graph contains a perfect matching of significant color-bias (i.e., a perfect matching that contains significantly more than half of its edges in one color). In this note we prove an analogous result for perfect matchings in k-uniform hypergraphs. More precisely, for each 2 ≤ ℓ < k and r ≥ 2 we determine the minimum ℓ-degree threshold for forcing a perfect matching of significant color-bias in an r-colored k-uniform hypergraph.
AB - A result of Balogh et al. yields the minimum degree threshold that ensures a 2- colored graph contains a perfect matching of significant color-bias (i.e., a perfect matching that contains significantly more than half of its edges in one color). In this note we prove an analogous result for perfect matchings in k-uniform hypergraphs. More precisely, for each 2 ≤ ℓ < k and r ≥ 2 we determine the minimum ℓ-degree threshold for forcing a perfect matching of significant color-bias in an r-colored k-uniform hypergraph.
KW - color-bias
KW - discrepancy
KW - perfect matchings
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U2 - 10.1137/24M1637350
DO - 10.1137/24M1637350
M3 - Article
AN - SCOPUS:85206258713
SN - 0895-4801
VL - 38
SP - 2543
EP - 2552
JO - SIAM Journal on Discrete Mathematics
JF - SIAM Journal on Discrete Mathematics
IS - 4
ER -