Graph classes: a survey
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
On graph powers for leaf-labeled trees
Journal of Algorithms
Strictly chordal graphs are leaf powers
Journal of Discrete Algorithms
Structure and linear-time recognition of 4-leaf powers
ACM Transactions on Algorithms (TALG)
Leaf Powers and Their Properties: Using the Trees
ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
Structure and linear time recognition of 3-leaf powers
Information Processing Letters
On relaxing the constraints in pairwise compatibility graphs
WALCOM'12 Proceedings of the 6th international conference on Algorithms and computation
On pairwise compatibility graphs having Dilworth number two
Theoretical Computer Science
Hi-index | 5.23 |
A graph G=(V,E) is called a pairwise compatibility graph (PCG) if there exists a tree T, a positive edge weight function w on T, and two non-negative real numbers d"m"i"n@?d"m"a"x, such that each leaf l"u of T corresponds to a vertex u@?V and there is an edge (u,v)@?E if and only if d"m"i"n@?d"T","w(l"u,l"v)@?d"m"a"x where d"T","w(l"u,l"v) is the sum of the weights of the edges on the unique path from l"u to l"v in T. In this paper we analyze the class of PCGs in relation to two particular subclasses resulting from the cases where the constraints on the distance between the pairs of leaves concern only d"m"a"x (LPG) or only d"m"i"n (mLPG). In particular, we show that the union of LPG and mLPG classes does not coincide with the whole class of PCGs, their intersection is not empty, and that neither of the classes LPG and mLPG is contained in the other. Finally, we study the closure properties of the classes PCG, mLPG and LPG, under some common graph operations. In particular, we consider the following operations: adding an isolated or universal vertex, adding a pendant vertex, adding a false or a true twin, taking the complement of a graph and taking the disjoint union of two graphs.