## Abstract NebeskΓ½ in [12] show that for any simple graph with __n__ β₯ 5 vertices, either __G__ or __G^c^__ contains an eulerian subgraph with order at least __n__ β 1, with an explicitly described class of exceptional graphs. In this note, we show that if __G__ is a simple graph with __n__ β₯ 61 v
Supereulerian graphs and excluded induced minors
β Scribed by Hong-Jian Lai
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 494 KB
- Volume
- 146
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
β¦ Synopsis
We show that if a graph G with r'(G) 1> 2 does not have an induced subgraph contractible to K2, 3 or to one of the subdivided wheels, then G has a spanning eulerian subgraph. As a corollary, such a graph has a nowhere-zero 4-flow.
π SIMILAR VOLUMES
Any 3-edge-connected graph with at most 10 edge cuts of size 3 either has a spanning closed trail or it is contractible to the Petersen graph.
## Abstract A graph is __supereulerian__ if it has a spanning eulerian subgraph. There is a rduction method to determine whether a graph is supereulerian, and it can also be applied to study other concepts, e.g., hamiltonian line graphs, a certain type of double cycle cover, and the total interval
Let G be a graph, and let H be a connected subgraph of G. When it is known that the graph G/H (obtained from G by contracting H to a vertex) has a spanning eulerian subgraph, under what conditions can it be inferred that G itself has a spanning eulerian subgraph? 0 1996 John Wiley & Sons, Inc.
## Abstract For any graph __H__, let Forb\*(__H__) be the class of graphs with no induced subdivision of __H__. It was conjectured in [J Graph Theory, 24 (1997), 297β311] that, for every graph __H__, there is a function __f__~__H__~: βββ such that for every graph __G__βForb\*(__H__), Ο(__G__)β€__f__