Vertex-disjoint copies of K¯₄

• Autorzy: Ken-ichi Kawarabayashi
• Języki publikacji: EN

Abstrakty

EN

Let G be a graph of order n. Let K¯ₗ be the graph obtained from Kₗ by removing one edge.
In this paper, we propose the following conjecture:
Let G be a graph of order n ≥ lk with δ(G) ≥ (n-k+1)(l-3)/(l-2)+k-1. Then G has k vertex-disjoint K¯ₗ.
This conjecture is motivated by Hajnal and Szemerédi's [6] famous theorem. In this paper, we verify this conjecture for l=4.

Słowa kluczowe

EN

extremal graph theory; vertex disjoint copy; minimum degree

Kategorie tematyczne

• 05C70: Factorization, matching, partitioning, covering and packing
• 05C38: Paths and cycles

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2004
• Tom: 24
• Numer: 2
• Strony: 249-262

Daty

wydano

2004

otrzymano

2002-08-31

poprawiono

2004-02-06

Twórcy

autor

Ken-ichi Kawarabayashi

• Department of Mathematics, Faculty of Science and Technology, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan

Bibliografia

• [1] N. Alon and R. Yuster, H-factor in dense graphs, J. Combin. Theory (B) 66 (1996) 269-282, doi: 10.1006/jctb.1996.0020.
• [2] G.A. Dirac, On the maximal number of independent triangles in graphs, Abh. Math. Semin. Univ. Hamb. 26 (1963) 78-82, doi: 10.1007/BF02992869.
• [3] Y. Egawa and K. Ota, Vertex-Disjoint $K_{1,3}$ in graphs, Discrete Math. 197/198 (1999), 225-246.
• [4] Y. Egawa and K. Ota, Vertex-disjoint paths in graphs, Ars Combinatoria 61 (2001) 23-31.
• [5] Y. Egawa and K. Ota, $K_{1,3}$-factors in graphs, preprint.
• [6] A. Hajnal and E. Szemerédi, Proof of a conjecture of P. Erdős, Colloq. Math. Soc. János Bolyai 4 (1970) 601-623.
• [7] K. Kawarabayashi, K¯₄-factor in a graph, J. Graph Theory 39 (2002) 111-128, doi: 10.1002/jgt.10007.
• [8] K. Kawarabayashi, F-factor and vertex disjoint F in a graph, Ars Combinatoria 62 (2002) 183-187.
• [9] J. Komlós, Tiling Túran theorems, Combinatorica 20 (2000) 203-218.

Identyfikatory

DOI

10.7151/dmgt.1229