Some Ramsey theorems for finite n-colorable and n-chromatic graphs
نویسنده
چکیده
Given a fixed integer n, we prove Ramsey-type theorems for the classes of all finite ordered n-colorable graphs, finite n-colorable graphs, finite ordered n-chromatic graphs, and finite n-chromatic graphs.
منابع مشابه
Size of edge-critical uniquely 3-colorable planar graphs
A graph G is uniquely k-colorable if the chromatic number of G is k and G has only one k-coloring up to permutation of the colors. A uniquely k-colorable graph G is edge-critical if G − e is not a uniquely k-colorable graph for any edge e ∈ E(G). Mel’nikov and Steinberg [L. S. Mel’nikov, R. Steinberg, One counterexample for two conjectures on three coloring, Discrete Math. 20 (1977) 203-206] as...
متن کاملReu 2007
Bn : (∀x1, . . . , xn)( if all xi are distinct then the subgraph induced on x1, . . . , xn is 3-colorable). By Erdős-DeBruijn, the countable set of axioms Bn (n = 1, 2, . . . ) defines 3-colorability. To show that 3-colorability is not finitely axiomatizable, we show the (apparently) stronger result that non-3-colorability is not axiomatizable. To do this, we use ultraproducts. It suffices to c...
متن کاملDense triangle-free graphs are four-colorable: A solution to the Erdős-Simonovits problem
In 1972, Erdős and Simonovits [9] asked whether a triangle-free graph with minimum degree greater than n/3, where n is the number of vertices, has chromatic number at most three. Hajnal provided examples of triangle-free graphs with arbitrarily large chromatic number and minimum degree greater than (1/3− ε)n, for every ε > 0. Häggkvist [10] gave a counterexample to the Erdős-Simonovits problem ...
متن کاملGraphs with Tiny Vector Chromatic Numbers and Huge Chromatic Numbers
Karger, Motwani and Sudan (JACM 1998) introduced the notion of a vector coloring of a graph. In particular they show that every k-colorable graph is also vector kcolorable, and that for constant k, graphs that are vector kcolorable can be colored by roughly 1 2=k colors. Here is the maximum degree in the graph. Their results play a major role in the best approximation algorithms for coloring an...
متن کاملLarge Chromatic Number and Ramsey Graphs
Let Q(n, χ) denote the minimum clique size an n-vertex graph can have if its chromatic number is χ . Using Ramsey graphs we give an exact, albeit implicit, formula for the case χ ≥ (n + 3)/2.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Contributions to Discrete Mathematics
دوره 5 شماره
صفحات -
تاریخ انتشار 2010