On 1-rotational decompositions of complete graphs into tripartite graphs

• Autorzy: Bunge Ryan C.

Identyfikatory

DOI

10.7494/OpMath.2019.39.5.623

• Języki publikacji: EN

Abstrakty

EN

Consider a tripartite graph to be any simple graph that admits a proper vertex coloring in at most 3 colors. Let G be a tripartite graph with n edges, one of which is a pendent edge. This paper introduces a labeling on such a graph G used to achieve 1-rotational G-decompositions of K2nt for any positive integer t. It is also shown that if G with a pendent edge is the result of adding an edge to a path on n vertices, then G admits such a labeling.

Słowa kluczowe

EN

graph decomposition; 1-rotational; vertex labeling

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2019
• Tom: Vol. 39, no. 5
• Strony: 623--643
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Bunge Ryan C.

• Illinois State University Department of Mathematics Normal, IL 61790-4520, USA

Bibliografia

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• [2] R.C. Bunge, A. Chantasartrassmee, S.I. El-Zanati, C. Vanden Eynden, On cyclic decompositions of complete graphs into tripartite graphs, J. Graph Theory 72 (2013), 90-111.
• [3] R.C. Bunge, S.I. El-Zanati, W. O'Hanlon, C. Vanden Eynden, On ^/-labeling the almost bipartite graph Pm + e, Ars Combin. 107 (2012), 65-80.
• [4] S.I. El-Zanati, C. Vanden Eynden, On Rosa-type labelings and cyclic graph decompositions, Mathematica Slovaca 59 (2009), 1-18.
• [5] S.I. El-Zanati, C. Vanden Eynden, N. Punnim, On the cyclic decomposition of complete graphs into bipartite graphs, Australas. J. Combin. 24 (2001), 209-219.
• [6] J.A. Gallian, A dynamic survey of graph labeling, Electron. J. Combin. 20 (2017), Dynamic Survey 6, 432 pp., http://www.combinatorics.org/ojs/index.php/eljc/ article/view/DS6.
• [7] A. Rosa, On certain valuations of the vertices of a graph, in: Theorie des graphes, journees internationales d'etudes, Rome 1966 (Dunod, Paris, 1967), 349-355.