# 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}
}```
• Published in
Discussiones Mathematicae…
31 January 2012
• Mathematics
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

## Figures from this paper

• Mathematics
2015 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.
• Mathematics
J. 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.
• Mathematics
Ninth 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
• Mathematics
ArXiv
• 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.
• Mathematics
World 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
• Mathematics
Proceedings 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
• Mathematics
ArXiv
• 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

• Mathematics
J. 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
• Mathematics
ArXiv
• 2011
In this paper interval edge-colorings of various graph products are investigated.
• Mathematics
ArXiv
• 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.
• Mathematics
ArXiv
• 2007
In this paper interval edge colorings of bipartite cylinders and bipartites tori are investigated.
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.
• Mathematics