The list-chromatic number and the coloring number of uncountable graphs
We study the list-chromatic number and the coloring number of graphs, especially uncountable graphs. We show that the coloring number of a graph coincides with its list-chromatic number provided that…
Reverse Mathematics and the Coloring Number of Graphs
- MathematicsNotre Dame J. Formal Log.
Methods of reverse mathematics are used to analyze the proof theoretic strength of a theorem involving the notion of coloring number, stating that if a graph is the union of n forests, then the coloring number of the graph is at most 2n.
Colouring problems of Erdos and Rado on infinite graphs
Colouring problems of Erdős and Rado on infinite graphs Dániel T. Soukup Doctor of Philosophy Graduate Department of Mathematics University of Toronto 2015 The aim of this thesis is to provide…
Universality in Graph Properties with Degree Restrictions
- MathematicsDiscuss. Math. Graph Theory
A k-degenerate graph is constructed which is universal for the induced-hereditary property of finite k- Degenerate graphs and the notion of a property with assignment is introduced and studied.
Good point sequencings of Steiner triple systems
An ℓ -good sequencing of a Steiner triple system of order v , STS( v ), is a permutation of the points of the system such that no ℓ consecutive points in the permutation contains a block. It is known…
Constructions of infinite graphs with Ramsey property
- MathematicsJ. Graph Theory
For every infinite cardinal λ and 2 ≤ n < ω there is a directed graph D of size λ such that D does not contain directed circuits of length ≤n and if its vertices are colored with
INFINITE COMBINATORICS PLAIN AND SIMPLE
- MathematicsThe Journal of Symbolic Logic
The main purpose is to demonstrate the ease and wide applicability of the general method based on trees of elementary submodels in a form accessible to anyone with a basic background in set theory and logic.
Orientations of graphs with uncountable chromatic number
- MathematicsJ. Graph Theory
It is proved that consistently there are digraphs with uncountable dichromatic number and arbitrarily large digirth; this is in surprising contrast with the undirected case: any graph with unccountable chromatic number contains a 4-cycle.
A note on generalized chromatic number and generalized girth
- MathematicsDiscret. Math.
SHOWING 1-10 OF 28 REFERENCES
Graph Theory and Probability
- MathematicsCanadian Journal of Mathematics
A well-known theorem of Ramsay (8; 9) states that to every n there exists a smallest integer g(n) so that every graph of g(n) vertices contains either a set of n independent points or a complete…
C. Berge, Théorie des graphes et ses applications. VIII + 277 S. m. 117 Abb. Paris 1958. Dunod Editeur. Preis geb. 3400 F
From accessible to inaccessible cardinals (Results holding for all accessible cardinal numbers and the problem of their extension to inaccessible ones)