## 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__ (βcycleβ means here: edge disjoint sum of elementary cycles). As a corollary we obtain the characterization of sub
A note on graphs spanned by Eulerian graphs
β 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.
β¦ 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 NPβcomplete. 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.
π SIMILAR VOLUMES
## 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
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
## Abstract An application of conservative graphs to topological graph theory is indicated.
## 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
## 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