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Showing 1 to 5 of 5 for “"critical graphs"”.
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Ultraconnected and Critical Graphs
… investigate the ultraconnectivity condition on graphs, and provide further connections between critical and ultraconnected graphs in the positive definite partial matrix completion problem. We completely characterize when the join of graphs is ultraconnected, and prove that ultraconnectivity is …
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Sparse color-critical graphs and rainbow matchings in edge-colored graphs
Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2013-04-05T19:14:32Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 26 THESIS_04.tex: 303472 bytes, checksum: ac02fb44aef43edf6047cfd6a308c01b (MD5) Setup.pdf: 26974 bytes, checksum: …
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Extremal Problems in Graph Theory: Hamiltonicity, Minimum Vertex -Diameter -2 -Critical Graphs and Decomposition
… graph K n can be decomposed into k spanning subgraphs with the t-star property. We prove that ift≥3and k≥68+t,then ft,k ≥32˙2 tk+25-10t ˙2t-2-3. .
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Dynamic coloring of graphs
… consider are the chromatic number of important graphs, upper bounds of the chromatic number, vertex-critical graphs, and stable graphs. For these first three subjects, we prove theorems for dynamic colorings that are similar to important theorems known for proper colorings, while we show no such …
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Coloring and constructing (hyper)graphs with restrictions
We consider questions regarding the existence of graphs and hypergraphs with certain coloring properties and other structural properties. In Chapter 2 we consider color-critical graphs that are nearly bipartite and have few edges. We prove a conjecture of Chen, Erdős, Gyárfás, and Schelp concerning …