Geodesic
Proper distinguishing colorings with few colors for graphs with girth at least 5
Daniel W. Cranston1
1Virginia Commonwealth University
The electronic journal of combinatorics, Tome 25 (2018) no. 3
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The distinguishing chromatic number, $\chi_D(G)$, of a graph $G$ is the smallest number of colors in a proper coloring, $\varphi$, of $G$, such that the only automorphism of $G$ that preserves all colors of $\varphi$ is the identity map. Collins and Trenk conjectured that if $G$ is connected with girth at least 5 and $G\ne C_6$, then $\chi_D(G)\leqslant \Delta+1$. We prove this conjecture.
DOI : 10.37236/7170
Classification : 05C15, 05C25
Mots-clés : distinguishing chromatic number, automorphism, distinguishing coloring, girth 5, greedy coloring

Daniel W. Cranston  1

1 Virginia Commonwealth University 
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Daniel W. Cranston. Proper distinguishing colorings with few colors for graphs with girth at least 5. The electronic journal of combinatorics, Tome 25 (2018) no. 3. doi: 10.37236/7170

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