We show that the minimum set of unordered graphs that must be forbidden to get the same graph class characterized by forbidding a single ordered graph is infinite.
On minimal forbidden subgraph characterizations of balanced graphs
✍ Scribed by Bonomo, Flavia; Durán, Guillermo; Safe, Martín D.; Wagler, Annegret K.
- Book ID
- 122509044
- Publisher
- Elsevier Science
- Year
- 2013
- Tongue
- English
- Weight
- 624 KB
- Volume
- 161
- Category
- Article
- ISSN
- 0166-218X
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
## Abstract A path graph is the intersection graph of subpaths of a tree. In 1970, Renz asked for a characterization of path graphs by forbidden induced subgraphs. We answer this question by determining the complete list of graphs that are not path graphs and are minimal with this property. © 2009
## Abstract Let ${\cal C}$ be a family of __n__ compact connected sets in the plane, whose intersection graph $G({\cal C})$ has no complete bipartite subgraph with __k__ vertices in each of its classes. Then $G({\cal C})$ has at most __n__ times a polylogarithmic number of edges, where the exponent