0
$\begingroup$

Hello everyone. I'm really struggling with this question. All help appreciated.

Find the minimum positive integer r for which there exists an r-regular graph G such that λ(G) ≥ κ(G) + 2

I know it's not 1,2,3-regular since κ(G) = λ(G) for those graphs.

$\endgroup$
  • $\begingroup$ This is a homework question: google.com/… $\endgroup$ – domotorp Apr 9 '12 at 8:11
  • $\begingroup$ Actually it's an exercise from Chartrand & Lesniak Ex2.4 Q.16, and it's not homework. $\endgroup$ – janvdl Apr 9 '12 at 8:32
  • 2
    $\begingroup$ I'd suggest you put such question on math.stackexchange.com . $\endgroup$ – Jernej Apr 9 '12 at 9:14
  • $\begingroup$ Just consider all the possibilities, there are very few. $\endgroup$ – Brendan McKay Apr 9 '12 at 14:56
1
$\begingroup$

Take tow disjoint copies of the complete graph on 5 vertices. Pick a vertex on each of the copy and split into tow vertices of degree 2. Match the the degree 2 vertices of both copies the identify them to get 4-regular, 4-egde-connected, and 2-vertex-connected graph.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.