منابع مشابه
On Some Conjectures of Griggs and Graffiti
We discuss a conjecture of J. R. Griggs relating the maximum number of leaves in a spanning tree of a simple, connected graph to the order and independence number of the graph. We prove a generalization of this conjecture made by the computer program Graffiti, and discuss other similar conjectures, including several generalizations of the theorem that the independence number of a simple, connec...
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Variable-length codes are the bases of the free submonoids of a free monoid. There are some important longstanding open questions about the structure of finite maximal codes. In this paper we discuss this conjectures and their relations with factorizations of cyclic groups.
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1. Notation. Let Z and N be the sets of integers and positive integers respectively. For b, c ∈ Z the Lucas sequences {U n (b, c)} and {V n (b, c)} are defined by (1.1) U 0 (b, c) = 0, U 1 (b, c) = 1, U n+1 (b, c) = bU n (b, c) − cU n−1 (b, c) (n ≥ 1) and (1.2) V 0 (b, c) = 2, V 1 (b, c) = b, V n+1 (b, c) = bV n (b, c) − cV n−1 (b, c) (n ≥ 1). Let d = b 2 − 4c. It is well known that for n ∈ N, ...
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The complement of a graph G is denoted by G. χ(G) denotes the chromatic number and ω(G) the clique number of G. The cycles of odd length at least five are called odd holes and the complements of odd holes are called odd anti-holes. A graph G is called perfect if, for each induced subgraph G of G, χ(G) = ω(G). Classical examples of perfect graphs consist of bipartite graphs, chordal graphs and c...
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We express general conjectures for explicit forms of P-recurrences for the number of Young standard tableaux of height bounded by h. These recurrences are compatible with known results and Regev's asymptotic evaluations. Le but de cette note est essentiellement de pr esenter des conjectures ainsi que des indications sur les raisons qui nous ont port ees a les enoncer. Nos conjectures concernent...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1998
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(97)00093-9