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DTSTART:20230101T000000
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DTSTART;TZID=Asia/Seoul:20241217T163000
DTEND;TZID=Asia/Seoul:20241217T173000
DTSTAMP:20260417T234126
CREATED:20241115T062835Z
LAST-MODIFIED:20241115T064748Z
UID:10177-1734453000-1734456600@dimag.ibs.re.kr
SUMMARY:Joonkyung Lee (이준경)\, Counting homomorphisms in antiferromagnetic graphs via Lorentzian polynomials
DESCRIPTION:An edge-weighted graph $G$\, possibly with loops\, is said to be antiferromagnetic if it has nonnegative weights and at most one positive eigenvalue\, counting multiplicities. The number of graph homomorphisms from a graph $H$ to an antiferromagnetic graph $G$ generalises various important parameters in graph theory\, including the number of independent sets and proper vertex colourings. \nWe obtain a number of new homomorphism inequalities for antiferromagnetic target graphs $G$. In particular\, we prove that\, for any antiferromagnetic $G$\, \n$|\mathrm{Hom}(K_d\, G)|^{1/d} ≤ |\mathrm{Hom}(K_{d\,d} \setminus M\, G)|^{1/(2d)}$ \nholds\, where $K_{d\,d} \setminus M$ denotes the complete bipartite graph $K_{d\,d}$ minus a perfect matching $M$. This confirms a conjecture of Sah\, Sawhney\, Stoner and Zhao for complete graphs $K_d$. Our method uses the emerging theory of Lorentzian polynomials due to Brändén and Huh\, which may be of independent interest. \nJoint work with Jaeseong Oh and Jaehyeon Seo.
URL:https://dimag.ibs.re.kr/event/2024-12-17/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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