Rooted $K_4$-Minors

Details Rooted $K_4$-Minors Rooted $K_4$-Minors

2011-02-18

arxiv.org/abs/1102.3760v1

Mathematics

Combinatorics

Scientific paper

Let $a,b,c,d$ be four vertices in a graph $G$. A \emph{$K_4$-minor rooted} at $a,b,c,d$ consists of four pairwise-disjoint pairwise-adjacent connected subgraphs of $G$, respectively containing $a,b,c,d$. We characterise precisely when $G$ contains a $K_4$-minor rooted at $a,b,c,d$ by describing six classes of obstructions, which are the edge-maximal graphs containing no $K_4$-minor rooted at $a,b,c,d$. The following two special cases illustrate the full characterisation: (1) A 4-connected non-planar graph contains a $K_4$-minor rooted at $a,b,c,d$ for every choice of $a,b,c,d$. (2) A 3-connected planar graph contains a $K_4$-minor rooted at $a,b,c,d$ if and only if $a,b,c,d$ are not on a single face.

Affiliated with

Also associated with

No associations

Rating

Rooted $K_4$-Minors 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 Rooted $K_4$-Minors, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Rooted $K_4$-Minors will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-211500