Cycle‐Saturated Graphs with Minimum Number of Edges |
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Authors: | Zoltán Füredi Younjin Kim |
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Affiliation: | 1. DEPARTMENT OF MATHEMATICS, UNIVERSITY OF ILLINOIS, , URBANA, ILLINOIS;2. RéNYI INSTITUTE OF MATHEMATICS OF THE HUNGARIAN, ACADEMY OF SCIENCES, , BUDAPEST, P.O. BOX 127 HUNGARY;3. DEPARTMENT OF MATHEMATICS, UNIVERSITY OF ILLINOIS AT URBANA‐CHAMPAIGN, , URBANA, ILLINOIS |
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Abstract: | A graph G is called H‐saturated if it does not contain any copy of H, but for any edge e in the complement of G, the graph contains some H. The minimum size of an n‐vertex H‐saturated graph is denoted by . We prove holds for all , where is a cycle with length k. A graph G is H‐semisaturated if contains more copies of H than G does for . Let be the minimum size of an n‐vertex H‐semisaturated graph. We have We conjecture that our constructions are optimal for . © 2012 Wiley Periodicals, Inc. J. Graph Theory 73: 203–215, 2013 |
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Keywords: | graphs cycles extremal graphs minimal saturated graphs |
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