Let G be a simple graph with n≥4 vertices and d(x)+d(y)≥n+k for each edge xy∈E(G). In this work we prove that G either contains a spanning closed trail containing any given edge set X if ∣X∣≤k, or G is a well characterized graph. As a corollary, we show that line graphs of such graphs are k-hamiltonian.
@article{arxiv.1706.07274,
title = {A note on edge degree and spanning trail containing given edges},
author = {Weihua Yang and Hong-jian Lai and Baoyindureng Wu},
journal= {arXiv preprint arXiv:1706.07274},
year = {2017}
}