1. CMB Online first
|Coloring Four-uniform Hypergraphs on Nine Vertices|
Every 4-uniform hypergraph on 9 vertices with at most 25 edges has property B. This gives the answer $m_9(4)=26$ to a question raised in 1968 by ErdÅs.
Keywords:property B, coloring hypergraphs
2. CMB 2011 (vol 56 pp. 265)
|Embedding Distributions of Generalized Fan Graphs|
Total embedding distributions have been known for a few classes of graphs. Chen, Gross, and Rieper computed it for necklaces, close-end ladders and cobblestone paths. Kwak and Shim computed it for bouquets of circles and dipoles. In this paper, a splitting theorem is generalized and the embedding distributions of generalized fan graphs are obtained.
Keywords:total embedding distribution, splitting theorem, generalized fan graphs
3. CMB 1998 (vol 41 pp. 348)
|Characterizing continua by disconnection properties |
We study Hausdorff continua in which every set of certain cardinality contains a subset which disconnects the space. We show that such continua are rim-finite. We give characterizations of this class among metric continua. As an application of our methods, we show that continua in which each countably infinite set disconnects are generalized graphs. This extends a result of Nadler for metric continua.
Keywords:disconnection properties, rim-finite continua, graphs
Categories:54D05, 54F20, 54F50