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Almost-Rainbow Edge-Colorings of Some Small Subgraphs

Elliot Krop, Irina Krop (2013)

Discussiones Mathematicae Graph Theory

Let f(n, p, q) be the minimum number of colors necessary to color the edges of Kn so that every Kp is at least q-colored. We improve current bounds on these nearly “anti-Ramsey” numbers, first studied by Erdös and Gyárfás. We show that [...] , slightly improving the bound of Axenovich. We make small improvements on bounds of Erdös and Gyárfás by showing [...] and for all even n ≢ 1(mod 3), f(n, 4, 5) ≤ n− 1. For a complete bipartite graph G= Kn,n, we show an n-color construction to color the edges...

Atoms and partial orders of infinite languages

Werner Kuich, N. W. Sauer (2001)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We determine minimal elements, i.e., atoms, in certain partial orders of factor closed languages under ⊆ . This is in analogy to structural Ramsey theory which determines minimal structures in partial orders under embedding.

Atoms and partial orders of infinite languages

Werner Kuich, N. W. Sauer (2010)

RAIRO - Theoretical Informatics and Applications

We determine minimal elements, i.e., atoms, in certain partial orders of factor closed languages under ⊆. This is in analogy to structural Ramsey theory which determines minimal structures in partial orders under embedding.

Avoiding rainbow 2-connected subgraphs

Izolda Gorgol (2017)

Open Mathematics

While defining the anti-Ramsey number Erdős, Simonovits and Sós mentioned that the extremal colorings may not be unique. In the paper we discuss the uniqueness of the colorings, generalize the idea of their construction and show how to use it to construct the colorings of the edges of complete split graphs avoiding rainbow 2-connected subgraphs. These colorings give the lower bounds for adequate anti-Ramsey numbers.

Chvátal-Erdos condition and pancyclism

Evelyne Flandrin, Hao Li, Antoni Marczyk, Ingo Schiermeyer, Mariusz Woźniak (2006)

Discussiones Mathematicae Graph Theory

The well-known Chvátal-Erdős theorem states that if the stability number α of a graph G is not greater than its connectivity then G is hamiltonian. In 1974 Erdős showed that if, additionally, the order of the graph is sufficiently large with respect to α, then G is pancyclic. His proof is based on the properties of cycle-complete graph Ramsey numbers. In this paper we show that a similar result can be easily proved by applying only classical Ramsey numbers.

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