# Interval Edge-Colorings of Cartesian Products of Graphs I

@inproceedings{Khachatrian2013IntervalEO, title={Interval Edge-Colorings of Cartesian Products of Graphs I}, author={Hrant Khachatrian and Petros A. Petrosyan and Hovhannes Tananyan}, booktitle={Discuss. Math. Graph Theory}, year={2013} }

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.

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