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| Date: | Mon, 3 Jun 2002 10:02:20 -0400 |
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Dear Colleagues,
We continue our Colloquium.
Dr. Lucas Van der Merwe
Department of Mathematics,
Northeast State Community College
3-Domination Critical Graphs with Arbitrary Independent Domination Numbers
June 4, Tuesday, Room 159, 11:45 am.
Abstract. Sumner and Blitch conjectured in 1983 that for any $k-$domination
critical graph $G$ with $k\ge 3,\;\gamma(G)=i(G)=k.$ This conjecture was
disproved in 1996 for $k\ge 4$ by Ao, Cockayne, MacGillivray and Mynhardt,
leaving the conjecture open only for $k=3.$ We show that there exists a
connected 3-domination critical graph $G$ with $i(G)=k$ for each $k\ge 3,$
thus settling the conjecture.
The speaker is a candidate for a position at the Department of Mathematics.
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