DECOMPOSITIONS OF COMPLETE GRAPHS INTO KAYAK PADDLES

Dalibor Froncek; Leah Tollefson

doi:10.22342/jims.0.0.17.39-44

Dalibor Froncek ⁽¹⁾ , Leah Tollefson ⁽²⁾

(1) University of Minnesota, United States,

(2) University of Minnesota, United States

https://doi.org/10.22342/jims.0.0.17.39-44

Issue
Special Edition, Year 2011

Submitted
March 9, 2012

Accepted
March 9, 2012

Published
March 9, 2012

Keywords:

Graph decomposition, graceful labeling, rosy labeling

ABSTRACT FULL PAPER

Abstract

A canoe paddle is a cycle attached to an end-vertex of a path. It was shown by Truszczynski that all canoe paddles are graceful and therefore decompose complete graphs. A kayak paddle is a pair of cycles joined by a path. We prove that the complete graph K<sub>2n+1</sub> is decomposable into kayak paddles with <i>n</i> edges whenever at least one of its cycles is eve.

DOI : http://dx.doi.org/10.22342/jims.0.0.17.39-44

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Authors

Dalibor Froncek

University of Minnesota

author@jims-a.org (Primary Contact)

Leah Tollefson

University of Minnesota

Author Biographies

Dalibor Froncek, University of Minnesota

Department of Mathematics and Statistics

Leah Tollefson, University of Minnesota

Department of Mathematics and Statistics

Froncek, D., & Tollefson, L. (2012). DECOMPOSITIONS OF COMPLETE GRAPHS INTO KAYAK PADDLES. Journal of the Indonesian Mathematical Society, 39–44. https://doi.org/10.22342/jims.0.0.17.39-44