A Note on (3,1)-Choosable Toroidal Graphs

Details A Note on (3,1)-Choosable Toroidal Graphs A Note on (3,1)-Choosable Toroidal Graphs

2006-09-27

arxiv.org/abs/math/0609757v1

Mathematics

Combinatorics

7 pages

Scientific paper

An $(L,d)^*$-coloring is a mapping $\phi$ that assigns a color $\phi(v)\in L(v)$ to each vertex $v\in V(G)$ such that at most $d$ neighbors of $v$ receive colore $\phi(v)$. A graph is called $(m,d)^*$-choosable, if $G$ admits an $(L,d)^*$-coloring for every list assignment $L$ with $|L(v)|\geq m$ for all $v\in V(G)$. In this note, it is proved that every toroidal graph, which contains no adjacent triangles and contains no 6-cycles and $l$-cycles for some $l \in \{5,7\}$, is $(3,1)^*$-choosable.

Affiliated with

Also associated with

No associations

Rating

A Note on (3,1)-Choosable Toroidal 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 A Note on (3,1)-Choosable Toroidal Graphs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Note on (3,1)-Choosable Toroidal Graphs will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-167833