منابع مشابه
On Induced Subgraphs with All Degrees Odd
Gallai proved that the vertex set of any graph can be partitioned into two sets, each inducing a subgraph with all degrees even. We prove that every connected graph of even order has a vertex partition into sets inducing subgraphs with all degrees odd, and give bounds for the number of sets of this type required for vertex partitions and vertex covers. We also give results on the partitioning a...
متن کاملLarge Induced Subgraphs with All Degrees Odd
We prove that every connected graph of order n ≥ 2 has an induced subgraph with all degrees odd of order at least cn/ log n, where c is a constant. We also give a bound in terms of chromatic number, and resolve the analogous problem for random graphs.
متن کاملInduced Subgraphs With Many Distinct Degrees
Let hom(G) denote the size of the largest clique or independent set of a graph G. In 2007, Bukh and Sudakov proved that every n-vertex graph G with hom(G) = O(log n) contains an induced subgraph with Ω(n) distinct degrees, and raised the question of deciding whether an analogous result holds for every n-vertex graph G with hom(G) = O(n), where ε > 0 is a fixed constant. Here, we answer their qu...
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It is proved that every tree T on n > 2 vertices contains an induced subgraph F such that all its degrees are odd and 1 F 1 >rn/21,
متن کاملInduced subgraphs of Ramsey graphs with many distinct degrees
An induced subgraph is called homogeneous if it is either a clique or an independent set. Let hom(G) denote the size of the largest homogeneous subgraph of a graph G. In this short paper we study properties of graphs on n vertices with hom(G) ≤ C log n for some constant C. We show that every such graph contains an induced subgraph of order αn in which β √ n vertices have different degrees, wher...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1994
ISSN: 0012-365X
DOI: 10.1016/0012-365x(92)00563-7