## 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 the Petersen Graph
β Scribed by Paul A. Catlin; Hong-Jian Lai
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 619 KB
- Volume
- 66
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
β¦ Synopsis
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.
π SIMILAR VOLUMES
## 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
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.
## Abstract A graph Ξ is locally Petersen if, for each point __t__ of Ξ, the graph induced by Ξ on all points adjacent to __t__ is isomorphic to the Petersen graph. We prove that there are exactly three isomorphism classes of connected, locally Petersen graphs and further characterize these graphs
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.