منابع مشابه
On k-ordered graphs
Ng and Schultz [J Graph Theory 1 (1997), 45±57] introduced the idea of cycle orderability. For a positive integer k, a graph G is k-ordered if for every ordered sequence of k vertices, there is a cycle that encounters the vertices of the sequence in the given order. If the cycle is also a Hamiltonian cycle, then G is said to be k-ordered Hamiltonian. We give sum of degree conditions for nonadja...
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A hamiltonian graph G of order n is k-ordered, 2 ≤ k ≤ n, if for every sequence v1, v2, . . . , vk of k distinct vertices of G, there exists a hamiltonian cycle that encounters v1, v2, . . . , vk in this order. Theorems by Dirac and Ore, presenting sufficient conditions for a graph to be hamiltonian, are generalized to k-ordered hamiltonian graphs. The existence of k-ordered graphs with small m...
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An ordered graph is a graph equipped with a linear ordering of its vertex set. A pair of ordered graphs is Ramsey finite if it has only finitely many minimal ordered Ramsey graphs and Ramsey infinite otherwise. Here an ordered graph F is an ordered Ramsey graph of a pair (H,H ′) of ordered graphs if for any coloring of the edges of F in colors red and blue there is either a copy of H with all e...
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Let V be a set of n points in R2. The θ-graph of V is a geometric graph with vertex set V that has been studied extensively and which has several nice properties. We introduce a new variant of θ-graphs which we call ordered θ-graphs. These are graphs that are built incrementally by inserting the vertices one by one so that the resulting graph depends on the insertion order. We show that careful...
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An ordered graph G< is a graph G with vertices ordered by the linear ordering <. The ordered Ramsey number R(G<, c) is the minimum number N such that every ordered complete graph with c-colored edges and at least N vertices contains a monochromatic copy of G<. For unordered graphs it is known that Ramsey numbers of graphs with degrees bounded by a constant are linear with respect to the number ...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2011
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2010.11.018