# Interval Edge-Colorings of Cartesian Products of Graphs I

@inproceedings{Khachatrian2012IntervalEO, title={Interval Edge-Colorings of Cartesian Products of Graphs I}, author={Hrant Khachatrian and Petros A. Petrosyan and Hovhannes Tananyan}, booktitle={Discussiones Mathematicae Graph Theory}, year={2012} }

Abstract A proper edge-coloring of a graph G with colors 1, . . . , t is an interval t-coloring if all colors are used and the colors of edges incident to each vertex of G form an interval of integers. A graph G is interval colorable if it has an interval t-coloring for some positive integer t. Let be the set of all interval colorable graphs. For a graph G ∈ , the least and the greatest values of t for which G has an interval t-coloring are denoted by w(G) and W(G), respectively. In this paper…

## 19 Citations

### On interval edge-colorings of bipartite graphs

- Mathematics2015 Computer Science and Information Technologies (CSIT)
- 2015

It is shown that all bipartite graphs on 15 vertices are interval colorable, and it is observed that several classes of bipartites of small order have an interval coloring.

### Some results on cyclic interval edge colorings of graphs

- MathematicsJ. Graph Theory
- 2018

It is proved that all complete multipartite graphs admit cyclic interval colorings; this settles in the affirmative, a conjecture of Petrosyan and Mkhitaryan.

### On interval edge-colorings of complete tripartite graphs

- MathematicsNinth International Conference on Computer Science and Information Technologies Revised Selected Papers
- 2013

An edge-coloring of a graph G with colors 1, ..., t is an interval t-coloring if all colors are used, and the colors of edges incident to each vertex of G are distinct and form an interval of…

### Some parameters related to the deficiency of graphs and the deficiency of near-complete graphs

- MathematicsArXiv
- 2016

Some bounds are obtained on wdef (G) and Wdef ( G) for connected graphs based on the conjecture that if n ∈ N, then def(K2n+1− e) = n− 1, and this paper confirms this conjecture.

### INTERVAL EDGE-COLORING OF COMPLETE AND COMPLETE BIPARTITE GRAPHS WITH RESTRICTIONS

- MathematicsWorld Science
- 2021

An edge-coloring of a graph G with consecutive integers c1,…,ct is called an interval t-coloring, if all colors are used, and the colors of edges incident to any vertex of G are distinct and form an…

### INTERVAL EDGE-COLORINGS OF TREES WITH RESTRICTIONS ON THE EDGES

- MathematicsProceedings of the YSU A: Physical and Mathematical Sciences
- 2021

An edge-coloring of a graph $G$ with consecutive integers $c_1,\ldots,c_t$ is called an interval t-coloring, if all colors are used, and the colors of edges incident to any vertex of $G$ are distinct…

### On the deficiency of complete multipartite graphs

- MathematicsArXiv
- 2019

A tight upper bound is obtained for the deficiency of complete multipartite graphs, which is the minimum number of pendant edges whose attachment to G leads to a graph admitting an interval coloring.

## References

SHOWING 1-10 OF 25 REFERENCES

### A note on upper bounds for the maximum span in interval edge-colorings of graphs

- MathematicsDiscret. Math.
- 2012

### Interval edge-colorings of complete graphs and n-dimensional cubes

- MathematicsDiscret. Math.
- 2010

### Investigation on Interval Edge-Colorings of Graphs

- MathematicsJ. Comb. Theory, Ser. B
- 1994

An edge-coloring of a simple graph G with colors 1, 2,..., t is called an interval t-coloring 3] if at least one edge of G is colored by color i, i = 1, ..., t and the edges incident with each vertex…

### Interval edge-colorings of graph products

- MathematicsArXiv
- 2011

In this paper interval edge-colorings of various graph products are investigated.

### Interval colorings of edges of a multigraph

- MathematicsArXiv
- 2014

The Proposition holds, since if t > w(G) then an interval on V (G) (t − 1)-coloring can be obtained from an intervalon V (g) t-coloring by recoloring with the color t − �(G), and all edges colored by t are recolored.

### Lower bounds for the greatest possible number of colors in interval edge colorings of bipartite cylinders and bipartite tori

- MathematicsArXiv
- 2007

In this paper interval edge colorings of bipartite cylinders and bipartites tori are investigated.

### Interval edge colorings of some products of graphs

- MathematicsDiscuss. Math. Graph Theory
- 2011

It is shown that the product of a set of graphs G,H 2 N, then the Cartes楡n product of these graphs be汯ngs to N, where N is the set of a汬 楮terval co-��rab汥 graphs.

### On Topological Invariants of the Product of Graphs

- MathematicsCanadian Mathematical Bulletin
- 1969

We consider ordinary graphs, that is, finite, undirected graphs with no loops or multiple lines. The product (also called cartesian product [4]) G1 × G2 of two graphs G1 and G2 with point sets V1 and…

### Interval colorings of complete bipartite graphs and trees

- MathematicsArXiv
- 2013

A translation from Russian of the work of R.R. Kamalian "Interval colorings of complete bipartite graphs and trees", Preprint of the Computing Centre of the Academy of Sciences of Armenia, Yerevan,…