Home > RHUMJ > Vol. 18 (2017) > Iss. 1

#### Article Title

#### Abstract

A word *w* =*uu* is called a long square if *u* is of length at least 3; a word *w* is called long-square-free if *w* contains no sub-word that is a long square. If there exists a *k*-coloring of the vertices of a graph *G* such that, for any path *P* in *G*, the word generated by the coloring of *P* is long-square-free, then *G* is called long-repetition-free} *k*-colorable. We show that every rooted tree of radius *r* <= 7 is long-repetition-free 2-colorable. We also show that there exists a class of trees which are not long-repetition-free 2-colorable.

#### Sponsor

David Milan, Associate Professor of Mathematics, The University of Texas at Tyler

#### Recommended Citation

Antonides, Joseph; Kiers, Claire; and Yamzon, Nicole
(2017)
"On the Long-Repetition-Free 2-Colorability of Trees,"
*Rose-Hulman Undergraduate Mathematics Journal*: Vol. 18
:
Iss.
1
, Article 15.

Available at:
http://scholar.rose-hulman.edu/rhumj/vol18/iss1/15