Let X be a set of v elements (v≥3). A transitive triple from X is a collection of three ordered pairs (x, y), (y, z)and (x, z), where x, y and z are distinct dements of X. It is denoted by (x, y, z). A transitive tri...Let X be a set of v elements (v≥3). A transitive triple from X is a collection of three ordered pairs (x, y), (y, z)and (x, z), where x, y and z are distinct dements of X. It is denoted by (x, y, z). A transitive triple system on X is a pair (X, B), where B is a collection of transitive triples from X such that each ordered pair of distinct elements of X belongs to exactly one transitive triple of B. The system is denoted by TTS(v). It is well known that the spectrum for TTS(v)is the set of all v≡0, 1 (mod 3).展开更多
At the Fourth International Conference on Graph Theory and Applications (1980), G. Chartrand posed the following problem: If a graph G contains spanning trees with m and n end-vertices, respecfively, where m<n, doe...At the Fourth International Conference on Graph Theory and Applications (1980), G. Chartrand posed the following problem: If a graph G contains spanning trees with m and n end-vertices, respecfively, where m<n, does G contain a spanning tree with k end-vertices for every integer k where m< k<n? Recently, the problem has been settled by S. Schuster and Cai Maocheng, independently. Here we shall introduce a simpler proof.展开更多
In the theoretical study on the stability of autonomous regulated system, A.Y. Lurbi and V. N. Laonuenov put forward the problem of stability in the large of trivial solution of the following equation:
文摘Let X be a set of v elements (v≥3). A transitive triple from X is a collection of three ordered pairs (x, y), (y, z)and (x, z), where x, y and z are distinct dements of X. It is denoted by (x, y, z). A transitive triple system on X is a pair (X, B), where B is a collection of transitive triples from X such that each ordered pair of distinct elements of X belongs to exactly one transitive triple of B. The system is denoted by TTS(v). It is well known that the spectrum for TTS(v)is the set of all v≡0, 1 (mod 3).
文摘At the Fourth International Conference on Graph Theory and Applications (1980), G. Chartrand posed the following problem: If a graph G contains spanning trees with m and n end-vertices, respecfively, where m<n, does G contain a spanning tree with k end-vertices for every integer k where m< k<n? Recently, the problem has been settled by S. Schuster and Cai Maocheng, independently. Here we shall introduce a simpler proof.
文摘In the theoretical study on the stability of autonomous regulated system, A.Y. Lurbi and V. N. Laonuenov put forward the problem of stability in the large of trivial solution of the following equation:
