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Complexity of finding embeddings in a k -tree
This work determines the complexity status of two problems related to finding the smallest number k such that a given graph is a partial k-tree and presents an algorithm with polynomially bounded (but exponential in k) worst case time complexity.
Complement reducible graphs
Modeling interactome: scale-free or geometric?
It is shown that the structure of PPI networks is better modeled by a geometric random graph than by a scale-free model, and a random geometric model provides a much more accurate model of the PPI data.
A Linear Recognition Algorithm for Cographs
This paper presents a linear time algorithm for recognizing cographs and constructing their cotree representation, which is possible to design very fast polynomial time algorithms for problems which are intractable for graphs in general.
It is shown that a tree 1-spanner, if it exists, in a weighted graph with $m$ edges and $n$ vertices is a minimum spanning tree and can be found in $O(m \log \beta(m, n)$ time, and the problem of determining the existence of a tree $t$- spanner in a Weighted graph is proven to be NP-complete.
Clustering and domination in perfect graphs
Asteroidal Triple-Free Graphs
This paper argues that the property of being AT-free is what is enforcing the linear ordering of the vertex sets of asteroidal triple-free graphs and presents various structural properties and characterizations of AT- free graphs.
A Unified View of Graph Searching
This paper unifies the view of graph search algorithms by showing simple, closely related characterizations of various well-known search paradigms, including BFS and DFS, and these characterizations naturally lead to other search paradigsms, namely, maximal neighborhood search and LexDFS.
Simple Linear Time Recognition of Unit Interval Graphs
The graph isomorphism disease
The present state of the art of isomorphism testing is surveyed, its relationship to NP-completeness is discussed, and some of the difficulties inherent in this particularly elusive and challenging problem are indicated.