Traceability on 2-connected line graphs

摘要

In this paper, we mainly prove the following: Let G be a connected almost bridgeless simple graph of order n sufficiently large such that σ¯2(G)=min{d(u)+d(v):uv∈E(G)}≥2(⌊n/11⌋−1). Then either L(G) is traceable or Catlin’s reduction of the core of G is one of eight graphs of order 10 or 11, where the core of G is obtained from G by deleting the vertices of degree 1 of G and replacing each path of length 2 whose internal vertex has degree 2 in G by an edge. We also give a new proof for the similar theorem in Niu et al. (2012) which has flaws in their proof.