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Supereulerian Graphs and the Petersen Graph

✍ 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.

✦ 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.


πŸ“œ SIMILAR VOLUMES


Supereulerian complementary graphs
✍ Hong-Jian Lai πŸ“‚ Article πŸ“… 1993 πŸ› John Wiley and Sons 🌐 English βš– 541 KB

## 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__ ‐ 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: A survey
✍ Paul A. Catlin πŸ“‚ Article πŸ“… 1992 πŸ› John Wiley and Sons 🌐 English βš– 996 KB

## 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

Supereulerian graphs and excluded induce
✍ Hong-Jian Lai πŸ“‚ Article πŸ“… 1995 πŸ› Elsevier Science 🌐 English βš– 494 KB

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.

The ubiquitous Petersen graph
✍ Gary Chartrand; HΓ©ctor Hevia; Robin J. Wilson πŸ“‚ Article πŸ“… 1992 πŸ› Elsevier Science 🌐 English βš– 507 KB
Locally petersen graphs
✍ J. I. Hall πŸ“‚ Article πŸ“… 1980 πŸ› John Wiley and Sons 🌐 English βš– 684 KB

## 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

A reduction criterion for supereulerian
✍ Catlin, Paul A. πŸ“‚ Article πŸ“… 1996 πŸ› John Wiley and Sons 🌐 English βš– 162 KB πŸ‘ 2 views

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.