I am seeking assistance with a research paper on Conflict-free k-edge coloring (CFEC). While I am familiar with the definition of Conflict-free k-vertex coloring, I have been unable to locate any credible sources that define CFEC. As a result, I attempted to derive a parallel definition of CFEC from CFVC. However, my professor has expressed concerns about the validity of my definition and has instructed me not to create definitions on my own.
Below is the definition of CFVC from the paper of Seymour Conflict-free Vertex Coloring of Planar Graphs;
A conflict-free k-vertex-coloring of a simple graph G is the $c: {1,2,...,k} \rightarrow V' \subseteq V$ such that for every $v \in V$, there is a $v' \in N(v)$ where the color of $v'$ is unique in the neighborhood of $v$. The set $V \setminus V'$ represents the uncolored vertices.
Here is the definition of CFEC I made parallel to the definition of CFVC;
A conflict-free k-edge-coloring of a simple graph G is the c: ({1,2,...,k} \rightarrow E' \subseteq E) such that for every (e \in E), there is an (e' \in N(e)) where the color of e’ is unique in the neighborhood of e. The set $E \backslash E'$ represents the uncolored edges.
Therefore, I am reaching out to the community to inquire if there is an established definition of CFEC or if someone can guide me to a reputable source that provides one. Any help would be greatly appreciated.
Thank you.
Have you tried this paper :
J. Czap, S. Jendrol’, and J. Valiska, “Conflict-free connections of graphs,” Discussiones Mathematicae Graph Theory, vol. 38, no. 4, pp. 911–920, 2018, doi: 10.7151/dmgt.2036.
Looks like it has the definition you're looking for, and it comes from a reputable source.