An algebraic theory of graph factorization
โ Scribed by Andrew Vince
- Publisher
- Elsevier Science
- Year
- 1983
- Tongue
- English
- Weight
- 136 KB
- Volume
- 46
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
โฆ Synopsis
An algebraic theory of graph factorization is introduced. For a factor h, a graph G(h) is constructod whose structure contains information about h-factorability. The l-factorable and cycle factorable graphs over Z2 are characterized, and properties of the corresponding graph G(h) are obtained.
๐ SIMILAR VOLUMES
We give necessary and sufficient conditions that the complete graph K, has an isomorphic factorization into Kr X K,. We show that this factorization has an application to clone library screening.
Let a and b be integers such that 0 s a s b. Then a graph G is called an [a,bl-graph if a 6 dG(x) s b for every x E V(G), and an [a,b]-factor of a graph is defined to be its spanning subgraph F such that a d dF(x) d b for every vertex x, where dG(x) and dJx) denote the degrees of x in G and F, respe
## Abstract A cycle in a graph is a set of edges that covers each vertex an even number of times. A cocycle is a collection of edges that intersects each cycle in an even number of edges. A bicycle is a collection of edges that is both a cycle and a cocycle. The cycles, cocycles, and bicycles each
We introduce and start the study of a bialgebra of graphs, which we call the 4-bialgebra, and of the dual bialgebra of 4-invariants. The 4-bialgebra is similar to the ring of graphs introduced by W. T. Tutte in 1946, but its structure is more complicated. The roots of the definition are in low dimen