Crux and long cycles in graphs

We introduce a notion of the crux of a graph G, measuring the order of a smallest dense subgraph in G. This simple-looking notion leads to some generalisations of known results about cycles, offering an interesting paradigm of ‘replacing average degree by crux’. In particular, we prove that every gr...

Full description

Bibliographic Details
Main Authors: Haslegrave, JGE, Hu, J, Kim, J, Liu, H, Luan, B, Wang, G
Format: Journal article
Language:English
Published: Society for Industrial and Applied Mathematics 2022