## Abstract Vizing's conjecture from 1968 asserts that the domination number of the Cartesian product of two graphs is at least as large as the product of their domination numbers. In this paper we survey the approaches to this central conjecture from domination theory and give some new results alo
A survey: Recent results, conjectures, and open problems in labeling graphs
β Scribed by Joseph A. Gallian
- Publisher
- John Wiley and Sons
- Year
- 1989
- Tongue
- English
- Weight
- 752 KB
- Volume
- 13
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
β¦ Synopsis
In this paper we organize and summarize much of the work done on graceful and harmonious labelings of graphs. Many open problems and conjectures are included.
π SIMILAR VOLUMES
This paper aims to give a brief introduction to a set of problems, old and new, concerned with one of the main and long-standing quests in infinite graph theory: how to represent the end structure of a given graph by that of a simpler subgraph, in particular a spanning tree. There has been a fair am
In Section 1, we survey the existence theorems for a kernel; in Section 2, we discuss a new conjecture which could constitute a bridge between the kernel problems and the perfect graph conjecture. In fact, we believe that a graph is 'quasi-perfect' if and only if it is perfect. ## Proposition 1.1.
We consider a matrix analogue of Schur's conjecture concerning permutation polynomials induced by polynomials with integral coefficients. For any fixed integer \(m \geq 1\) we consider polynomials with integral coefficients which induce permutations on the ring of all \(m \times m\) matrices over th
## Abstract Ramsey's theorem guarantees that if __G__ is a graph, then any 2βcoloring of the edges of a large enough complete graph yields a monochromatic copy of __G__. Interesting problems arise when one asks how many such __G__ must occur. A survey of this and related problems is given, along wi