𝔖 Bobbio Scriptorium
✦   LIBER   ✦

A note on graphs spanned by Eulerian graphs

✍ Scribed by W. R. Pulleyblank


Publisher
John Wiley and Sons
Year
1979
Tongue
English
Weight
109 KB
Volume
3
Category
Article
ISSN
0364-9024

No coin nor oath required. For personal study only.

✦ Synopsis


Abstract

We show that the problem raised by Boesch, Suffel, and Tindell of determining whether or not a graph is spanned by an Eulerian subgraph is NP‐complete. We also note that there does exist a good algorithm for determining if a graph is spanned by a subgraph having positive even degree at every node.


πŸ“œ SIMILAR VOLUMES


A Note on Sub-Eulerian Graphs
✍ F. Jaeger πŸ“‚ Article πŸ“… 1979 πŸ› John Wiley and Sons 🌐 English βš– 114 KB

## Abstract We present an algebraic proof of the following result: a set of edges of a multigraph __G__ is contained in some cycle of __G__ iff the set contains no odd cocycle of __G__ (β€œcycle” means here: edge disjoint sum of elementary cycles). As a corollary we obtain the characterization of sub

The spanning subgraphs of eulerian graph
✍ F. T. Boesch; C. Suffel; R. Tindell πŸ“‚ Article πŸ“… 1977 πŸ› John Wiley and Sons 🌐 English βš– 312 KB

## Abstract It is shown that a connected graph __G__ spans an eulerian graph if and only if __G__ is not spanned by an odd complete bigraph __K__(2~m~ + 1, 2__n__ + 1). A disconnected graph spans an eulerian graph if and only if it is not the union of the trivial graph with a complete graph of odd

A note on graphs with diameter-preservin
✍ Fred Buckley; Martin Lewinter πŸ“‚ Article πŸ“… 1988 πŸ› John Wiley and Sons 🌐 English βš– 182 KB πŸ‘ 1 views

The distance between a pair of vertices u, u in a graph G is the length of a shortest path joining u and u. The diameter diam(G) of G is the maximum distance between all pairs of vertices in G. A spanning tree Tof G is diameter preserving if diam(T) = diam(G). In this note, we characterize graphs th

A note on conservative graphs
✍ Arthur T. White πŸ“‚ Article πŸ“… 1980 πŸ› John Wiley and Sons 🌐 English βš– 115 KB

## Abstract An application of conservative graphs to topological graph theory is indicated.

A note on coset graphs
✍ Ulrike Baumann πŸ“‚ Article πŸ“… 2011 πŸ› John Wiley and Sons 🌐 English βš– 90 KB

## Abstract Coset graphs are a generalization of Cayley graphs. They arise in the construction of graphs and digraphs with transitive automorphism groups. Moreover, the consideration of coset graphs makes it possible to give an algebraic description of regular connected graphs of even degree. In th

A Note on Graph Colorings and Graph Poly
✍ Noga Alon; Michael Tarsi πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 230 KB

## dedicated to professor w. t. tutte on the occasion of his eightieth birtday It is known that the chromatic number of a graph G=(V, E) with V= [1, 2, ..., n] exceeds k iff the graph polynomial f G => ij # E, i<j (x i &x j ) lies in certain ideals. We describe a short proof of this result, using