منابع مشابه
On a cycle partition problem
Let G be any graph and let c(G) denote the circumference of G. We conjecture that for every pair c1, c2 of positive integers satisfying c1 + c2 = c(G), the vertex set of G admits a partition into two sets V1 and V2, such that Vi induces a graph of circumference at most ci , i = 1, 2. We establish various results in support of the conjecture; e.g. it is observed that planar graphs, claw-free gra...
متن کاملA path(ological) partition problem
Let τ(G) denote the number of vertices in a longest path of the graph G and let k1 and k2 be positive integers such that τ(G) = k1+k2. The question at hand is whether the vertex set V (G) can be partitioned into two subsets V1 and V2 such that τ(G[V1]) ≤ k1 and τ(G[V2]) ≤ k2. We show that several classes of graphs have this partition property.
متن کاملThe satisfactory partition problem
The Satisfactory Partition problem consists in deciding if a given graph has a partition of its vertex set into two nonempty parts such that each vertex has at least as many neighbors in its part as in the other part. This problem was introduced by Gerber and Kobler [GK98, GK00] and further studied by other authors but its complexity remained open until now. We prove in this paper that Satisfac...
متن کاملThe Object Partition Problem
We provide a theoretical framework for the "object partition problem". We begin by considering this problem In a rather abstract context. Consider the semantic domain of physical objects, and the syntactic domain of picture graphs. The object partition problem can be viewed In terms of specifying syntactic operations that yield partitions of the picture graph, which when interpreted In the sema...
متن کاملSteinhaus’ Problem on Partition of a Triangle
H. Steinhaus has asked whether inside each acute triangle there is a point from which perpendiculars to the sides divide the triangle into three parts of equal areas. We present two solutions of Steinhaus’ problem. The n-dimensional case of Theorem 1 below was proved in [6], see also [2] and [4, Theorem 2.1, p. 152]. For an earlier mass-partition version of Theorem 1, for bounded convex masses ...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 1994
ISSN: 0022-314X
DOI: 10.1006/jnth.1994.1060