A graphG is calledrepresentable in a tree T, ifG is isomorphic to the intersection graph of a family of subtrees ofT. In this paper those graphs are characterized which are representable in some subdivision of theK 1,n. In the finite case polynomial-time recognition algorithms of these graphs are given. But this concept can be generalized to essentially infinite graphs by using no more trees but ‘tree-like’ posets and representability of graphs in these posets.
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Prisner, E. Representing triangulated graphs in stars. Abh.Math.Semin.Univ.Hambg. 62, 29–41 (1992). https://doi.org/10.1007/BF02941616
- Intersection Graph
- Interval Graph
- Cardinal Number
- Chordal Graph
- Star Graph