6 papers
Fixed-Defect Inverse Theorems for Subset Sums
Lizhong Chen
Let be an -element set of positive real numbers, let be its set of subset sums, and put . For every fixed integer and all sufficiently…
Exact Periodicity, Surjectivity, and a Haar Limit Law for a Restarting Josephus Process
Lizhong Chen
We study a restarting Josephus process in which the participants retain their linear order and counting restarts at the current leftmost survivor after every deletion. For step siz…
An infinite family of minimally nonperfectly divisible graphs with a bisimplicial vertex
Lizhong Chen
We disprove Hoàng's conjecture that a minimally nonperfectly divisible graph cannot contain a bisimplicial vertex by constructing an explicit infinite family. For every integer $t\…
Explicit and logarithmically improved chromatic bounds for -free graphs
Lizhong Chen
We prove that every \((P_2\cup P_3)\)-free graph \(G\), with \(k=ω(G)\), satisfies \[ χ(G)=O\!\left(k^3\frac{\ln\ln k}{\ln k}\right). \] Thus the class admits an \(o(k^3)\) binding…
Optimal chromatic bound for (, HVN)-free graphs
Lizhong Chen, Hongyang Wang
The HVN is a graph formed by removing two edges incident to the same vertex from the complete graph . In this paper, we prove that every (, HVN)-free graph sa…
Perfect divisions in (, bull)-free graphs
Lizhong Chen, Hongyang Wang
A graph has a perfect division if its vertex set can be partitioned into two sets , such that is perfect and . We call perfectly divisible if…