1. bookAHEAD OF PRINT
Journal Details
License
Format
Journal
eISSN
2083-5892
First Published
13 Apr 2013
Publication timeframe
4 times per year
Languages
English
access type Open Access

On a Graph Labelling Conjecture Involving Coloured Labels

Published Online: 10 Jan 2022
Volume & Issue: AHEAD OF PRINT
Page range: -
Received: 23 Jul 2021
Accepted: 15 Nov 2021
Journal Details
License
Format
Journal
eISSN
2083-5892
First Published
13 Apr 2013
Publication timeframe
4 times per year
Languages
English
Abstract

In this work, we investigate a recent conjecture by Baudon, Bensmail, Davot, Hocquard, Przyby lo, Senhaji, Sopena and Woźniak, which states that graphs, in general, can be edge-labelled with red labels 1, 2 and blue labels 1, 2 so that every two adjacent vertices are distinguished accordingly to either the sums of their incident red labels or the sums of their incident blue labels. To date, this was verified for several classes of graphs. Also, it is known how to design several labelling schemes that are very close to what is desired.

In this work, we adapt two important proofs of the field, leading to some progress towards that conjecture. We first prove that graphs can be labelled with red labels 1, 2, 3 and blue labels 1, 2 so that every two adjacent vertices are distinguished as required. We then verify the conjecture for graphs with chromatic number at most 4.

Keywords

MSC 2010

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