We prove that for C a finite set of cycles, there is a universal C-free graph if and only if C consists precisely of all the odd cycles of order less than same specified bound.
Graphs omitting a bushy tree
โ Scribed by Cherlin, G.; Shi, N.; Tallgren, L.
- Publisher
- John Wiley and Sons
- Year
- 1997
- Tongue
- English
- Weight
- 152 KB
- Volume
- 26
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
โฆ Synopsis
A tree is called bushy if it has no vertex of degree 2. Theorem: the class of countable graphs omitting a fixed finite bushy tree with at least 5 vertices has no universal element.
๐ SIMILAR VOLUMES
A connected graph G is a tree-clique graph if there exists a spanning tree T (a compatible tree) such that every clique of G is a subtree of T. When Tis a path the connected graph G is a proper interval graph which is usually defined as intersection graph of a family of closed intervals of the real
The author proved that, for c > 1, the random graph G(n, p ) on n vertices with edge probability p = c / n contains almost always an induced tree on at least q n ( 1 -o( 1)) vertices, where L Y ~ is the positive root of the equation CLY = log( 1 + c'a). It is shown here that if c is sufficiently lar
In this paper, we present the implementation of a branch-and-cut algorithm for solving Steiner tree problems in graphs. Our algorithm is based on an integer programming formulation for directed graphs and comprises preprocessing, separation algorithms, and primal heuristics. We are able to solve nea
Let Tp be any tree of order p and A ( T p ) stand for the maximum degree of the vertices of Tp. We prove the following theorem. "If A(Tp) 5 pi, where p > 2i, then Tp is i-placeable in Kp" is true if and only if i = 1, 2, and 3. 0 1996 John Wiley & Sons, Inc. Suppose G is a graph and V ( G ) , E ( G
The quantum mechanical relevance of the concept of a spanning tree extant within a given molecular graph-specifically, one that may be considered to represent the carbon-atom connectivity of a particular (planar) conjugated system-was first explicitly pointed out by Professor Roy McWeeny in his now-