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Claw-decomposition of Kneser Graphs | ||
| Transactions on Combinatorics | ||
| دوره 11، شماره 1، خرداد 2022، صفحه 53-61 اصل مقاله (973.52 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2021.126283.1792 | ||
| نویسندگان | ||
| Sankari C1؛ Sangeetha R* 1؛ K. Arthi2 | ||
| 1Department of Mathematics, A. V. V. M. Sri Pushpam College(Affiliated to Bharathidasan University), Poondi, Than- javur, Tamil Nadu, India | ||
| 2Department of Mathematics, A. V. V. M. Sri Pushpam College( Affiliated to Bharathidasan University), Poondi, Than- javur, Tamil Nadu, India | ||
| چکیده | ||
| A claw is a star with three edges. The Kneser graph $KG_{n,2}$ is the graph whose vertices are the $2$-subsets of an $n$-set, in which two vertices are adjacent if and only if their intersection is empty. In this paper, we prove that $KG_{n,2}$ is claw-decomposable, for all $n \geq 6$. | ||
| کلیدواژهها | ||
| Decomposition؛ Tensor Product؛ Kneser Graph؛ Crown Graph؛ Star | ||
| مراجع | ||
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[1] Y. Chen, Kneser graphs are Hamiltonian for n ≥ 3k, J. Combin. Theory Ser. B, 80 (2000) 69–79.
[2] S. Ganesamurthy and P. Paulraja, Existence of a P2k+1 -decomposition in the Kneser graph KGn,2 , Discrete Math., 341 (2018) 2113–2116. [3] M. Kneser, Aufgabe 360, Jahresbericht der Deutschen Mathematiker-Vereinigung, 2 58 (1955) pp. 27.
[4] C. Lin, J.-J. Lin and T.-W. Shyu, Isomorphic star decomposition of multicrowns and the power of cycles, Ars Combin., 53 (1999) 249–256. [5] C. A. Rodger and T. R. Whitt III, Path decompositions of Kneser and generalized Kneser graphs, Canad. Math. Bull., 58 (2015) 610–619. [6] I. Shields and C. D. Savage, A note on Hamilton cycles in Kneser graphs, Bull. Inst. Combin. Appl., 40 (2004) 13–22. [7] T. R. Whitt and C. A. Rodger, Decomposition of the Kneser graph into paths of length four, Discrete Math., 338 (2015) 1284–1288. [8] S. Yamamoto, H. Ikeda, S. Shige-eda, K. Ushio and N. Hamada, On claw-decomposition of complete graphs and complete bigraphs, Hiroshima Math. J., 5 (1975) 33–42. | ||
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