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… 
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Interval edge-colorings of complete graphs
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A new technique is introduced to construct interval colorings of complete graphs based on their 1-factorizations, which is used to disprove the conjecture, improve lower and upper bounds on W ( K 2 n ) and determine its exact values for n ź 12.
On interval edge-colorings of bipartite graphs
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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.
On interval edge-colorings of complete tripartite graphs
  • A. Grzesik, Hrant Khachatrian
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    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…
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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…
Further results on the deficiency of graphs
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It is shown that for any l ∈ N, there exists a graph G such that d e f ( G) > 0 and W d ef ( G ) − w d eF (G) ≥ l, and conjecture on the deficiency of near-complete graphs is confirmed.
On the deficiency of complete multipartite graphs
TLDR
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.
Interval edge-colorings of composition of graphs
TLDR
It is shown that all regular graphs, complete bipartite graphs and trees have such a special interval coloring of a special type, which implies that if G is a graph and T is a tree, then $G[T]\in \mathfrak{N}$.
Interval Total Colorings of Complete Multipartite Graphs and Hypercubes
TLDR
This paper proves that all complete multipartite graphs with the same number of vertices in each part are interval total colorable and gives some bounds for the minimum and the maximum span in interval totalcolorings of these graphs.
On Interval Edge-Colorings of Outerplanr Graphs
TLDR
This paper shows that if G is a 2-connected outerplanar graph with $\Delta(G)=3$, then $G$ is interval colorable and a negative answer to the question of Axenovich on theouterplanar triangulations is given.
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