- Tytuł:
- Universality in Graph Properties with Degree Restrictions
- Autorzy:
-
Broere, Izak
Heidema, Johannes
Mihók, Peter - Powiązania:
- https://bibliotekanauki.pl/articles/30146518.pdf
- Data publikacji:
- 2013-07-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
countable graph
universal graph
induced-hereditary
k-degenerate graph
graph with colouring number at most k + 1
graph property with assignment - Opis:
- Rado constructed a (simple) denumerable graph R with the positive integers as vertex set with the following edges: For given m and n with m < n, m is adjacent to n if n has a 1 in the m’th position of its binary expansion. It is well known that R is a universal graph in the set ℐc of all countable graphs (since every graph in ℐc is isomorphic to an induced subgraph of R). A brief overview of known universality results for some induced-hereditary subsets of ℐc is provided. We then construct a k-degenerate graph which is universal for the induced-hereditary property of finite k-degenerate graphs. In order to attempt the corresponding problem for the property of countable graphs with colouring number at most k + 1, the notion of a property with assignment is introduced and studied. Using this notion, we are able to construct a universal graph in this graph property and investigate its attributes.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2013, 33, 3; 477-492
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł