论文信息 - The number of kings in a multipartite tournament

The number of kings in a multipartite tournament

Abstract We show that in any n -partite tournament, where n ⩾ 3, with no transmitters and no 3-kings, the number of 4-kings is at least eight. All n -partite tournaments, where n ⩾ 3, having eight 4-kings and no 3-kings are completely characterized. This solves the problem proposed in Koh and Tan (accepted).

K. M. Koh | B. P. Tan | K. Koh | B. Tan

[1] Stephen B. Maurer. The King Chicken Theorems , 1980 .

[2] K. M. Koh,et al. Number of 4-kings in bipartite tournaments with no 3-kings , 1996, Discret. Math..

[3] D. Frank Hsu,et al. Graph Theory, Combinatorics, Algorithms, and Applications , 1991 .

[4] Wayne Goddard,et al. On multipartite tournaments , 1991, J. Comb. Theory, Ser. B.

[5] H. G. Landau,et al. On dominance relations and the structure of animal societies: II. Some effects of possible social factors , 1951 .

[6] K. M. Koh,et al. Kings in multipartite tournaments , 1995, Discret. Math..

[7] G. Gutin,et al. The radii of n-partite tournaments , 1986 .

[8] Carsten Thomassen,et al. Kings in k-partite tournaments , 1991, Discret. Math..

[9] Li Weixuan,et al. Toppling kings in a tournament by introducing new kings , 1987 .

[10] K. Brooks Reid. Every vertex a king , 1982, Discret. Math..

[11] Frank Harary,et al. Distance in graphs , 1990 .

[12] H. Landau. On dominance relations and the structure of animal societies: III The condition for a score structure , 1953 .

[13] Gregory Gutin,et al. Cycles and paths in semicomplete multipartite digraphs, theorems, and algorithms: a survey , 1995, J. Graph Theory.