Graph classes between parity and distance-hereditary graphs
نویسندگان
چکیده
منابع مشابه
Graph Classes between Parity and Distance-Hereditary Graphs
Several graph problems (e.g., steiner tree, connected domination, hamiltonian path, and isomorphism problem), which can be solved in polynomial time for distance-hereditary graphs, are NP-complete or open for parity graphs. Moreover, the metric characterizations of these two graph classes suggest an excessive gap between them. We introduce a family of classes forming an infinite lattice with re...
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A graph is shown to be distance-hereditary if and only if no induced subgraph of order five or more has a unique hamiltonian cycle; this is also equivalent to every induced subgraph of order five or more having an even number of hamiltonian cycles. Restricting the induced subgraphs to those of odd order five or more gives two similar characterizations of parity graphs. The close relationship be...
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In this work we introduce, characterize, and provide algorithmic results for (k, +)–distance-hereditary graphs, k ≥ 0. These graphs can be used to model interconnection networks with desirable connectivity properties; a network modeled as a (k, +)–distance-hereditary graph can be characterized as follows: if some nodes have failed, as long as two nodes remain connected, the distance between the...
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A graph G = (V,E) is called a probe graph of graph class G if V can be partitioned into two sets P (probes) and N (nonprobes), where N is an independent set, such that G can be embedded into a graph of G by adding edges between certain nonprobes. A graph is distance hereditary if the distance between any two vertices remains the same in every connected induced subgraph. Distancehereditary graph...
متن کاملDistance-hereditary graphs
Distance-hereditary graphs (sensu Howorka) are connected graphs in which all induced paths are isometric. Examples of such graphs are provided by complete multipartite graphs and ptolemaic graphs. Every finite distance-hereditary graph is obtained from K, by iterating the following two operations: adding pendant vertices and splitting vertices. Moreover, distance-hereditary graphs are character...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 1999
ISSN: 0166-218X
DOI: 10.1016/s0166-218x(99)00075-x