@article{Albert Khachik Sahakyan_2021, title={INTERVAL EDGE COLORING OF TREES WITH STRICT RESTRICTIONS ON THE SPECTRUMS}, url={https://rsglobal.pl/index.php/sr/article/view/2052}, DOI={10.31435/rsglobal_sr/30072021/7592}, abstractNote={<p>An edge-coloring of a graph <em>G</em> with consecutive integers <em>C<sub>1 </sub>,..., C<sub>t</sub></em> is called an interval <em>t</em>-coloring if all the colors are used, and the colors of edges incident to any vertex of <em>G</em> are distinct and form an interval of integers. A graph <em>G</em> is interval colorable if it has an interval <em>t</em>-coloring for some positive integer <em>t</em>. For an edge coloring <em>a</em> and a vertex <em>v</em> the set of all the colors of the incident edges of <em>v</em> is called the spectrum of that vertex in <em>a</em> and is denoted by <em>Sa</em>(<em>v</em>). We consider the case where the spectrum for each vertex <em>v</em> is provided <em>S</em>(<em>v</em>), and the problem is to find an edge-coloring <em>a</em> such that for every vertex <em>v</em>, <em>Sa</em>(<em>v</em>)=<em>S</em>(<em>v</em>). We provide an <em>O</em>(<em>N</em>) algorithm that finds such an edge-coloring for trees that satisfies all the restrictions. If it is impossible to have an edge-coloring that satisfies the restrictions of the spectrums the algorithm will tell that too.</p>}, number={3(38)}, journal={Science Review}, author={Albert Khachik Sahakyan}, year={2021}, month={Jun.} }