https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/664 2026-07-04T01:47:34Z https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/215896 Title: Unified almost linear kernels for generalized covering and packing problems on nowhere dense classes Authors: Ahn, Jungho; Kim, Jinha; Kwon, O-joung Abstract: Let F be a family of graphs and r≥0 be an integer. For a graph G and an integer k, (r,F)-COVERING asks whether there is a set D⊆V(G) of size at most k such that every induced subgraph of G isomorphic to a graph in F is at distance at most r from D. (r,F)-PACKING asks whether G has k induced subgraphs H1,…,Hk such that each Hi is isomorphic to a graph in F and the distance between distinct V(Hi) and V(Hj) in G is more than r. We show that for every fixed nonempty finite family F of connected graphs and r≥0, (r,F)-COVERING and (r,F)-PACKING admit almost linear kernels on every nowhere dense class of graphs, parameterized by the solution size k. As corollaries, we prove that DISTANCE-r VERTEX COVER, DISTANCE-r MATCHING, F-FREE VERTEX DELETION, and INDUCED-F-PACKING for any fixed finite family F of connected graphs admit almost linear kernels on every nowhere dense class of graphs. Our results extend the results for DISTANCE-r DOMINATING SET by Drange et al. (2016) [17] and Eickmeyer et al. (2017) [20] and for DISTANCE-r INDEPENDENT SET by Pilipczuk and Siebertz (2021) [41]. 2026-08-01T00:00:00Z https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/217772 Title: Ancient solutions to the Yamabe flow Authors: 김승혁 2026-06-23T00:00:00Z https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/217838 Title: Adaptive Boosting on Linear Networks Authors: 박선철 2026-06-15T00:00:00Z https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/210924 Title: Linear structures of norm-attaining Lipschitz functions and their complements Authors: Choi, Geunsu; Jung, Mingu; Lee, Han Ju; Roldan, Oscar Abstract: We solve two main questions on linear structures of (non-)norm-attaining Lipschitz functions. First, we show that for every infinite metric space M , the set consisting of Lipschitz functions on M which do not strongly attain their norm and the zero function contains an isometric copy of ℓ<inf>∞</inf>, and moreover, those functions can be chosen not to attain their norm as functionals on the Lipschitz-free space over M . Second, we prove that for every infinite metric space M , neither the set of strongly norm-attaining Lipschitz functions on M nor the union of its complement with zero is ever a linear space. Furthermore, we observe that the set consisting of Lipschitz functions which cannot be approximated by strongly norm-attaining ones and the zero element contains ℓ<inf>∞</inf> isometrically in all the known cases. Some natural observations and spaceability results are also investigated for Lipschitz functions that attain their norm in one way but do not in another. 2026-06-01T00:00:00Z