2024/01/30 by Dingding Dong, Dong, Dingding, Sammy Luo +1
Computer Science · #Advanced Graph Theory Research #Combinatorics (math.CO) #Complexity and Algorithms in Graphs #FOS: Mathematics #Network Packet Processing and Optimization
paper · pdf · doi:10.48550/arxiv.2401.16639
openalex publication_date 2024/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We say that a graph G is (k,ℓ)-stable if removing k vertices from it reduces its independence number by at most ℓ. We say that G is tight (k,ℓ)-stable if it is (k,ℓ)-stable and its independence number equals \lfloor(n-k+1)/(2)\rfloor+ℓ, the maximum possible, where n is the vertex number of G. Answering a question of Dong and Wu, we show that every tight (2,0)-stable graph with odd vertex number must be an odd cycle. Moreover, we show that for all k≥ 3, every tight (k,0)-stable graph has at most k+6 vertices.