Strong Chromatic Index of Outerplanar Graphs
Round 1
Reviewer 1 Report
The authors have provided an upper bound for the strong chromatic number for different classes of an outerplanar graph. Hocquard et al (2013) have shown that the strong chromatic number of an outerplanar graph is bounded by 3\Delta-3. In this paper, the authors have presented different types of graphs for which this value is exactly 3\Detla-3. This means that the 3\Delta-3 is a tight upper bound for outerplanar graphs. The result is interesting but it should be noted that Hocquard et al (2013) have already proved that 3\Delta-3 is a tight upper bound. In addition to this, the authors have also provided tight upper bounds for the strong chromatic number for bipartite outerplanar graphs.
I have some minor comments about the presentation of the manuscript. 1. In the abstract the authors should make it clear that the upper bound of 2\Delta for the bipartite outerplanar graph holds only if \Delta \geq 3. 2. Can the author provide some more definitions, such as that of clique-cut, in the introduction section to make the paper self-contained.Author Response
Please see the attachment.
Author Response File: 
Author Response.docx
Reviewer 2 Report
The paper is clearly written and presents new results. I only have some formal comments.
- Strong chromatic number or strong chromatic index? It's better to select one term.
- Why, except of Theorems and Lemmas, there are also Claims? What's the difference between a Claim and a Lemma here?
- There are two Claims 1: in Section 2 and Section 3. As far as numbering of lemmas does not restart with new section, numbering of claims also should not restart (or maybe the Claims will be re-named as Lemmas)
Author Response
Please see the attachment.
Author Response File: Author Response.docx
