2024/09/23 by Andrew Lane, Lane, Andrew, Natasha Morrison +1
Environmental Science · #Combinatorics (math.CO) #FOS: Mathematics #Forest ecology and management
paper · pdf · doi:10.48550/arxiv.2409.15275
openalex publication_date 2024/09/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a graph H, we say that a graph G is properly rainbow H-saturated if: (1) There is a proper edge colouring of G containing no rainbow copy of H; (2) For every e ∉ E(G), every proper edge colouring of G+e contains a rainbow copy of H. The proper rainbow saturation number sat^*(n,H) is the minimum number of edges in a properly rainbow H-saturated graph. In this paper we initiate a systematic study of the proper rainbow saturation number for trees. We obtain exact and asymptotic results on sat^*(n,T) for several infinite families of trees. Our proofs reveal connections to the classical saturation and semi-saturation numbers.