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On clique values identities and mantel-type theorems | ||
| Transactions on Combinatorics | ||
| مقاله 2، دوره 9، شماره 3، آذر 2020، صفحه 139-146 اصل مقاله (223.97 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2020.119553.1680 | ||
| نویسنده | ||
| Hossein Teimoori Faal* | ||
| Department of Mathematics and Computer Science, Allameh Tabatabai University, Tehran, Iran. | ||
| چکیده | ||
| In this paper, we first extend the weighted handshaking lemma, using a generalization of the concept of the degree of vertices to the values of graphs. This edge-version of the weighted handshaking lemma yields an immediate generalization of the Mantel's classical result which asks for the maximum number of edges in triangle-free graphs to the class of $K_{4}$-free graphs. Then, by defining the concept of value for cliques (complete subgraphs) of higher orders, we also extend the classical result of Mantel for any graph $G$. We finally conclude our paper with a discussion about the possible future works. | ||
| کلیدواژه‌ها | ||
| Reconstruction problem؛ vertex-deck؛ handshaking lemma؛ clique value identity | ||
| مراجع | ||
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[8] D. C. Fisher, The number of triangles in K4 -free graph, Disc. Math., 69 (1988) 203–205.
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[10] D. C. Fisher and J. Ryan, Bound on the number of complete subgraphs, Disc. Math., 103 (1992) 313–320.
[11] V. Nikiforov, The number of cliques in graphs of given order and size, Trans. Amer. Math. Soc., 363 (2011) 1599– 1618. [12] A. A. Razborov, On the minimal density of triangles in graphs, Combin. Prob. Comput., 17 (2008) 603–618. | ||
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آمار تعداد مشاهده مقاله: 180 تعداد دریافت فایل اصل مقاله: 206 |
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