𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Special monochromatic trees in two-colored complete graphs

✍ Scribed by Chen, Guantao; Schelp, Richard H.; ?olt�s, ?ubom�r

Publisher
John Wiley and Sons
Year
1997
Tongue
English
Weight
106 KB
Volume
24
Category
Article
ISSN
0364-9024

No coin nor oath required. For personal study only.

✦ Synopsis

For a positive integer k, a set of k + 1 vertices in a graph is a k-cluster if the difference between degrees of any two of its vertices is at most k -1. Given any tree T with at least k 3 edges, we show that for each graph G of sufficiently large order, either G or its complement contains a copy of T such that some vertices in the copy form a k-cluster in G. The same conclusion holds for any tree T having a vertex of degree more than k.

📜 SIMILAR VOLUMES

Properly colored hamilton cycles in edge
Properly colored hamilton cycles in edge-colored complete graphs
✍ N. Alon; G. Gutin 📂 Article 📅 1997 🏛 John Wiley and Sons 🌐 English ⚖ 156 KB 👁 2 views

It is shown that, for ⑀ ) 0 and n ) n ⑀ , any complete graph K on n vertices 0 ' Ž . whose edges are colored so that no vertex is incident with more than 1 y 1r 2 y ⑀ n edges of the same color contains a Hamilton cycle in which adjacent edges have distinct colors. Moreover, for every k between 3 and

Maximizing spanning trees in almost comp
Maximizing spanning trees in almost complete graphs
✍ Gilbert, Bryan; Myrvold, Wendy 📂 Article 📅 1997 🏛 John Wiley and Sons 🌐 English ⚖ 94 KB 👁 1 views

We examine the family of graphs whose complements are a union of paths and cycles and develop a very simple algebraic technique for comparing the number of spanning trees. With our algebra, we can obtain a simple proof of a result of Kel'mans that evening out path lengths increases the number of spa

Maximizing spanning trees in almost comp
Maximizing spanning trees in almost complete graphs
✍ Gilbert, Bryan; Myrvold, Wendy 📂 Article 📅 1997 🏛 John Wiley and Sons 🌐 English ⚖ 94 KB 👁 1 views

We examine the family of graphs whose complements are a union of paths and cycles and develop a very simple algebraic technique for comparing the number of spanning trees. With our algebra, we can obtain a simple proof of a result of Kel'mans that evening-out path lengths increases the number of spa

Remarks on the placeability of isomorphi
Remarks on the placeability of isomorphic trees in a complete graph
✍ Hasunuma, Toru; Shibata, Yukio 📂 Article 📅 1996 🏛 John Wiley and Sons 🌐 English ⚖ 99 KB 👁 2 views

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