Abstract
We determine the minimum size of n-factor-critical graphs and that of k-extendable bipartite graphs, by considering Harary graphs and related graphs. Moreover, we determine the minimum size of k-extendable non-bipartite graphs for k = 1, 2, and pose a related conjecture for general k.
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Research supported by NSFC (10801077), Natural Science Foundation of Guangdong Province (9451030007003340 and 9451009001002740), Natural Science Foundation of Jiangsu Higher Education Institutions of China (08KJB110008), and Science Research Foundation of Guangdong Industry Technical College.
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Zhang, ZB., Zhang, X., Lou, D. et al. Minimum Size of n-Factor-Critical Graphs and k-Extendable Graphs. Graphs and Combinatorics 28, 433–448 (2012). https://doi.org/10.1007/s00373-011-1045-y
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DOI: https://doi.org/10.1007/s00373-011-1045-y