For a fixed integer $m$, we consider edge colorings of complete graphs which contain no properly edge colored cycle $C_{m}$ as a subgraph. Within colorings free of these subgraphs, we establish global structure by bounding the number of colors that can induce a spanning and connected subgraph. In the case of smaller cycles, namely $C_4,C_5$, and $C_6$, we show that our bounds are sharp.
@article{10_37236_2304,
author = {Vincent Coll and Colton Magnant and Kathleen Ryan},
title = {Structure of colored complete graphs free of proper cycles},
journal = {The electronic journal of combinatorics},
year = {2012},
volume = {19},
number = {4},
doi = {10.37236/2304},
zbl = {1266.05027},
url = {http://geodesic.mathdoc.fr/articles/10.37236/2304/}
}
TY - JOUR
AU - Vincent Coll
AU - Colton Magnant
AU - Kathleen Ryan
TI - Structure of colored complete graphs free of proper cycles
JO - The electronic journal of combinatorics
PY - 2012
VL - 19
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/2304/
DO - 10.37236/2304
ID - 10_37236_2304
ER -
%0 Journal Article
%A Vincent Coll
%A Colton Magnant
%A Kathleen Ryan
%T Structure of colored complete graphs free of proper cycles
%J The electronic journal of combinatorics
%D 2012
%V 19
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/2304/
%R 10.37236/2304
%F 10_37236_2304
Vincent Coll; Colton Magnant; Kathleen Ryan. Structure of colored complete graphs free of proper cycles. The electronic journal of combinatorics, Tome 19 (2012) no. 4. doi: 10.37236/2304
