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…
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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,…