Anzeige
Erschienen in:
01.02.2016
Adjacent vertex-distinguishing edge coloring of 2-degenerate graphs
Erschienen in: Journal of Combinatorial Optimization | Ausgabe 2/2016
EinloggenAktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.
Wählen Sie Textabschnitte aus um mit Künstlicher Intelligenz passenden Patente zu finden. powered by
Markieren Sie Textabschnitte, um KI-gestützt weitere passende Inhalte zu finden. powered by
Abstract
The adjacent vertex-distinguishing chromatic index \(\chi '_{avd}(G)\) of a graph \(G\) is the smallest integer \(k\) for which \(G\) admits a proper edge \(k\)-coloring such that no pair of adjacent vertices are incident with the same set of colors. In this paper, we prove that if \(G\) is a \(2\)-degenerate graph without isolated edges, then \(\chi '_{avd} (G)\le \max \{6, \Delta (G)+1\}\). Moreover, we also show that when \(\Delta \ge 6\), \(\chi '_{avd}= \Delta (G)+1\) if and only if \(G\) contains two adjacent vertices of maximum degree.