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학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
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We consider a tournament T = (V,A). For each subset X of V is associated the subtournament T(X) = (X,A\(X×X)) of T induced by X. We say that a tournament T0 embeds into a tournament T when T0 is isomorphic to a subtournament of T. Otherwise, we say that T omits T0. A subset X of V is a clan of T provided that for a, b 2 X and x 2 V \X, (a, x) 2 A if and only if (b, x) 2 A. For example, ;, {x}(x 2 V )and V are clans of T, called trivial clans. A tournament is indecomposable if all its clans are trivial. In 2003, B. J. Latka characterized the class T of indecomposable tournaments omitting a certain tournament W5 on 5vertices. In the case of an indecomposable tournament T, we will study the set W5(T) of vertices x 2 V for which there exists a subset X of V such that x 2 X and T(X) is isomorphic to W5. We prove the following:for any indecomposable tournament T, if T 62 T , then |W5(T) | |V | −2and |W5(T) | |V | −1 if |V | is even. By giving examples, we also verify that this statement is optimal.
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참고문헌 (16)
참고문헌 신청
A. Benato / 2006 / On an adjacency property of almost all tournaments / Dis- crete Math 306 (19) : 2327 ~ 2335
A. Cournier / 1998 / Minimal indecomposable graphs / Discrete Math 183 (1) : 61 ~ 80
A. Ehrenfeucht / 1990 / Primitivity is hereditary for 2-structures / Theoret. Comput. Sci 70 (3) : 343 ~ 358
B. J. Latka / 2003 / Structure theorem for tournaments omitting N5 / J. Graph Theory 42 (3) : 165 ~ 192
C. Gnanvo / 1992 / La reconstruction des tournois sans diamants / Z. Math. Logik Grundlag. Math 38 (3) : 283 ~ 291
A. Cournier / 1998 / Minimal indecomposable graphs / Discrete Math 183 (1) : 61 ~ 80
A. Ehrenfeucht / 1990 / Primitivity is hereditary for 2-structures / Theoret. Comput. Sci 70 (3) : 343 ~ 358
B. J. Latka / 2003 / Structure theorem for tournaments omitting N5 / J. Graph Theory 42 (3) : 165 ~ 192
C. Gnanvo / 1992 / La reconstruction des tournois sans diamants / Z. Math. Logik Grundlag. Math 38 (3) : 283 ~ 291
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