منابع مشابه
Every Complete Binary Tree is Prime
A graph with a vertex set V is said to have a prime labeling if its vertices can be labeled with distinct integers 1; 2; ; jV j such that for every edge fx; yg, the labels assigned to x and y are relatively prime. A tree is prime if it has at least one prime labeling. Around 1980, Entringer conjectured that every tree is prime. After three decades, this conjecture remains open. Nevertheless, a ...
متن کامل4−equitable Tree Labelings
A tree is a vertex-edge graph that is connected and contains no cycles. A 4−equitable labeling of a graph is an assignment of labels {0, 1, 2, 3} to the vertices. The edge labels are the absolute difference of the labels of the vertices that they are incident to. The labels must be distributed as evenly as possible amongst the vertices and they must also be distributed as evenly as possible amo...
متن کاملWhen every $P$-flat ideal is flat
In this paper, we study the class of rings in which every $P$-flat ideal is flat and which will be called $PFF$-rings. In particular, Von Neumann regular rings, hereditary rings, semi-hereditary ring, PID and arithmetical rings are examples of $PFF$-rings. In the context domain, this notion coincide with Pr"{u}fer domain. We provide necessary and sufficient conditions for...
متن کاملEvery Monotone 3-Graph Property is Testable
Let k ≥ 2 be a fixed integer and P be a property of k-uniform hypergraphs. In other words, P is a (typically infinite) family of k-uniform hypergraphs and we say a given hypergraph H satisfies P if H ∈ P . For a given constant η > 0 a k-uniform hypergraph H on n vertices is η-far from P if no hypergraph obtained from H by changing (adding or deleting) at most ηn edges in H satisfies P . More pr...
متن کاملBehind Every Great Tree is a Great (Phylogenetic) Network
In Francis and Steel (2015), it was shown that there exists non-trivial networks on 4 leaves upon which the distance metric affords a metric on a tree which is not the base tree of the network. In this paper we extend this result in two directions. We show that for any tree T there exists a family of non-trivial HGT networks N for which the distance metric dN affords a metric on T . We addition...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2000
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(00)00033-9