منابع مشابه
Odd subgraphs and matchings
Let G be a graph and f : V (G) → {1, 3, 5, . . .}. Then a subgraph H of G is called a (1, f)-odd subgraph if degH(x) ∈ {1, 3, . . . , f(x)} for all x ∈ V (H). If f(x) = 1 for all x ∈ V (G), then a (1, f)-odd subgraph is nothing but a matching. A (1, f)-odd subgraph H of G is said to be maximum if G has no (1, f)-odd subgraph K such that |K| > |H|. We show that (1, f)-odd subgraphs have some pro...
متن کاملOptimal Matchings and Degree-Constrained Subgraphs
In this paper the term graph means a finite unoriented linear graph. The same symbol will be used for a graph and its edge-set. The degree d(v, G) of a vertex v in a graph G is simply the number of edges of G which are incident on v, with loops (edges from v to v) counted twice_ The term strict graph will be used for a graph whic h is loopless and contains at most one edge joining any pair of d...
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 کاملOn 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 کاملA pair of forbidden subgraphs and perfect matchings
In this paper, we study the relationship between forbidden subgraphs and the existence of a matching. Let H be a set of connected graphs, each of which has three or more vertices. A graph G is said to beH-free if no graph inH is an induced subgraph of G. We completely characterize the setH such that every connected H-free graph of sufficiently large even order has a perfect matching in the foll...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2002
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(01)00424-1