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… 

Figures from this paper

Interval edge-colorings of complete graphs

On interval edge-colorings of bipartite graphs

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

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

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

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

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

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

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

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

Investigation on Interval Edge-Colorings of Graphs

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

Consecutive colorings of the edges of general graphs

Interval edge-colorings of graph products

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

Interval colorings of edges of a multigraph

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

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

Interval edge colorings of some products of graphs

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.

A note on interval edge-colorings of graphs

If a connected graph G is a connected $r$-regular graph with $n$ vertices and has an interval $t$-coloring and $n\geq 2r+2$, then this upper bound can be improved to $2n-5.

On Topological Invariants of the Product of Graphs

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