Spectral radius and rainbow Hamiltonicity in bipartite graphs
Abstract
Let G=\G1, G2, … , Gk\ be a family of bipartite graphs on the same vertex set. A rainbow Hamilton path (cycle) in G is a path (cycle) that visits each vertex precisely once such that any two edges belong to different graphs of G. In this paper, by adopting the technique of bi-shifting, we present tight sufficient conditions in terms of the spectral radius for a family G to admit a rainbow Hamilton path and cycle, respectively. Meanwhile, we completely characterize the corresponding spectral extremal graphs.
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.