Intersection graphs of Helly families of subtrees

Subtrees and Subforests of Graphs

✍ S. Brandt 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 299 KB

In this paper we present sufficient edge-number and degree conditions for a graph to contain all forests of given size. The edge-number bound answers in the aflirmative a conjecture due to Erdős and Sós. Furthermore, we will give improved bounds for specified spanning subtrees of graphs. 1994 Academ

Largest size and union of Helly families

✍ Zsolt Tuza 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 557 KB

Intersection properties of graphs

✍ Terry A. McKee 📂 Article 📅 1991 🏛 Elsevier Science 🌐 English ⚖ 550 KB

McKee, T.A., Intersection properties of graphs, Discrete Mathematics 89 (1991) 253-260. For each graph-theoretic property, we define a corresponding 'intersection property', motivated by the natural relationship of paths with interval graphs, and of trees with chordal graphs. We then develop a simp

Intersection Graphs of Segments

✍ J. Kratochvil; J. Matousek 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 998 KB

Intersection graphs of segments (the class SEG) and of other simple geometric objects in the plane are considered. The results fall into two main areas: how difficult is the membership problem for a given class and how large are the pictures needed to draw the representations. Among others, we prove

Intersections of graphs

✍ Béla Bollobás; Alex Scott 📂 Article 📅 2011 🏛 John Wiley and Sons 🌐 English ⚖ 193 KB

Let G and H be two graphs of order n. If we place copies of G and H on a common vertex set, how much or little can they be made to overlap? The aim of this article is to provide some answers to this question, and to pose a number of related problems. Along the way, we solve a conjecture of Erd" os,

Induced subtrees in graphs of large chro

Induced subtrees in graphs of large chromatic number

✍ A. Gyárfás; E. Szemeredi; Zs. Tuza 📂 Article 📅 1980 🏛 Elsevier Science 🌐 English ⚖ 469 KB

Our paper proves special eases of the following conjecture: for any fined tr~,e "J~ there exists a natural number f = fiT) ~o that every triangle-free graph of chromatic number ] T) contains T as au induced subgraph. The main ;csult concerns the case when T has radius two.