Mathematics – Combinatorics
Scientific paper
2010-04-29
Mathematics
Combinatorics
Scientific paper
In 1990, Kostochka and Sidorenko proposed studying the smallest number of list-colorings of a graph $G$ among all assignments of lists of a given size $n$ to its vertices. We say a graph $G$ is $n$-monophilic if this number is minimized when identical $n$-color lists are assigned to all vertices of $G$. Kostochka and Sidorenko observed that all chordal graphs are $n$-monophilic for all $n$. Donner (1992) showed that every graph is $n$-monophilic for all sufficiently large $n$. We prove that all cycles are $n$-monophilic for all $n$; we give a complete characterization of 2-monophilic graphs (which turns out to be similar to the characterization of 2-choosable graphs given by Erdos, Rubin, and Taylor in 1980); and for every $n$ we construct a graph that is $n$-choosable but not $n$-monophilic.
Kirov Radoslav
Naimi Ramin
No associations
LandOfFree
List Coloring and $n$-monophilic graphs does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with List Coloring and $n$-monophilic graphs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and List Coloring and $n$-monophilic graphs will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-284466