Suppose the colors in a $\chi(G)$-coloring of a graph $G$ have been rearranged. We will call this rearrangement $c^*$.

The chromatic villainy of the $c^*$ is defined as the minimum number of vertices that need to be recolored in order to return $c^*$ to a proper coloring in which each color appears the same number of times as in the initial coloring.

The maximum chromatic villainy when considering all rearrangements of all $\chi(G)$-coloring of $G$ is the chromatic villainy of $G$.

Here, the chromatic villainies of certain families of graphs were investigated and the chromatic villainies of paths and certain classes of complete multipartite graphs were found.

Bounds were found for certain classes of odd cycles and complete multipartite graphs as well.

Library of Congress Subject Headings

Graph coloring; Paths and cycles (Graph theory)

Publication Date


Document Type


Student Type


Degree Name

Applied and Computational Mathematics (MS)

Department, Program, or Center

School of Mathematical Sciences (COS)


Paul Wenger

Advisor/Committee Member

Jobby Jacob

Advisor/Committee Member

Darren Narayan


RIT – Main Campus

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