## 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
Forbidden ordered subgraph vs. forbidden subgraph characterizations of graph classes
✍ Scribed by Ginn, Mark
- Publisher
- John Wiley and Sons
- Year
- 1999
- Tongue
- English
- Weight
- 88 KB
- Volume
- 30
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
✦ Synopsis
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.
📜 SIMILAR VOLUMES
## Abstract Given a set ${\cal F}$ of graphs, a graph __G__ is ${\cal F}$‐free if __G__ does not contain any member of ${\cal F}$ as an induced subgraph. We say that ${\cal F}$ is a degree‐sequence‐forcing set if, for each graph __G__ in the class ${\cal C}$ of ${\cal F}$‐free graphs, every realiza
Let S 1 ; S 2 ; . . . ; S t be pairwise disjoint non-empty stable sets in a graph H. The graph H Ã is obtained from H by: (i) replacing each S i by a new vertex q i ; (ii) joining each q i and q j , 1 i 6 ¼ j t, and; (iii) joining q i to all vertices in HÀ(S 1 [ S 2 [ Á Á Á [ S t ) which were adjace
## Abstract We characterize all pairs of connected graphs {__X__, __Y__} such that each 3‐connected {__X__, __Y__}‐free graph is pancyclic. In particular, we show that if each of the graphs in such a pair {__X__, __Y__} has at least four vertices, then one of them is the claw __K__~1,3~, while the
Various Hamiltonian-like properties are investigated in the squares of connected graphs free of some set of forbidden subgraphs. The star K,+ the subdivision graph of &, and the subdivision graph of K1,3 minus an endvertex play central roles. In particular, we show that connected graphs free of the