Journal of Combinatorial Mathematics and Combinatorial Computing
A graph G is collapsible if for every even subset R ⊆ V (G), there is a spanning connected subgraph HR of G whose set of odd degree vertices is R. A graph is reduced if it has no nontrivial collapsible subgraphs. Catlin  showed that the existence of spanning Eulerian subgraphs in a graph G can be determined by the reduced graph obtained from G by contracting all the collapsible subgraphs of G. In this paper, we present a result on 3-edge-connected reduced graphs of small orders. Then, we prove that a 3-edge-connected graph G of order n either has a spanning Eulerian subgraph or can be contracted to the Petersen graph if G satisfies one of the following:
(i) d(u) + d(v) > 2(n/15 − 1) for any uv 6∈ E(G) and n is large;
(ii) the size of a maximum matching in G is at most 6;
(iii) the independence number of G is at most 5.
These are improvements of prior results in , ,  and .
This is a post-print version of an article originally published in Journal of Combinatorial Mathematics and Combinatorial Computing, 2016, Volume 96.
The version of record is available through: WorldCat.
Chen, Wei-Guo and Chen, Zhi-Hong, "Spanning Eulerian subgraphs and Catlin’s reduced graphs" Journal of Combinatorial Mathematics and Combinatorial Computing / (2016): 41-63.
Available at https://digitalcommons.butler.edu/facsch_papers/1045