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Sufficient conditions for maximally edge-connected and super-edge-connected | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 4، دوره 2، شماره 1، شهریور 2017، صفحه 35-41 اصل مقاله (385.18 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2017.13594 | ||
| نویسندگان | ||
| Lutz Volkmann* 1؛ Zhen-Mu Hong2 | ||
| 1RWTH Aachen University | ||
| 2Anhui University of Finance and Economics | ||
| چکیده | ||
| Let $G$ be a connected graph with minimum degree $\delta$ and edge-connectivity $\lambda$. A graph is maximally edge-connected if $\lambda=\delta$, and it is super-edge-connected if every minimum edge-cut is trivial; that is, if every minimum edge-cut consists of edges incident with a vertex of minimum degree. In this paper, we show that a connected graph or a connected triangle-free graph is maximally edge-connected or super-edge-connected if the number of edges is large enough. | ||
| کلیدواژه‌ها | ||
| edge-connectivity؛ Maximally edge-connected graphs؛ Super-edge-connected graphs | ||
| مراجع | ||
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[2] G. Chartrand, A graph-theoretic approach to a communications problem, SIAM J. Appl. Math. 14 (1966), no. 4, 778–781.
[3] A. Hellwig and L. Volkmann, Maximally edge-connected and vertexconnected graphs and digraphs: A survey, Discrete Math. 308 (2008), no. 15, 3265–3296.
[4] A.K. Kelmans, Asymptotic formulas for the probability of k-connectedness of random graphs, Theory Probab. Appl. 17 (1972), no. 2, 243–254.
[5] W. Mantel, Problem 28, Wiskundige Opgaven 10 (1907), 60–61.
[6] P. Turán, On an extremal problem in graph theory (hungarian), Mat. Fiz. Lapok 48 (1941), 436–452.
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