Handle-rewriting hypergraph grammars

Discrete Applied Mathematics

Rotics

2015

A bubble model is a 2-dimensional representation of proper interval graphs. We consider proper interval graphs that have bubble models of specific properties. We characterise the maximal such proper interval graphs of bounded clique-width and of bounded linear cliquewidth and the minimal such proper interval graphs whose clique-width and linear cliquewidth exceed the bounds. As a consequence, we can efficiently compute the clique-width and linear clique-width of the considered graphs.

“…Observe that G must be almost like an induced path, informally spoken. By splitting G at b 1, 3 , it is not difficult to see that cwd(G) ≤ 3 holds.…”

Section: Characterisation and Computationmentioning

confidence: 99%

“…Clique-width is a graph width parameter with applications in efficient graph algorithms [3,4,20]. Clique-width generalises treewidth in the sense that graphs of bounded treewidth also have bounded clique-width [5], but graphs of bounded clique-width may have unbounded treewidth.…”

Section: Introductionmentioning

confidence: 99%

Clique-width of full bubble model graphs

Discrete Applied Mathematics

Rotics

2015

“…Clique-width was introduced by Courcelle, Engelfriet, Rozenberg [5]. The clique-width of a graph G, denoted by cwd(G), is defined as the smallest number of labels needed to construct G, using the following operations:…”

Section: Upper Bounds On the Clique-width Of Proper Interval Graphsmentioning

confidence: 99%

A new representation of proper interval graphs with an application to clique-width

Heggernes

Electronic Notes in Discrete Mathematics

Papadopoulos

2009

“…Clique-width is a graph parameter that describes the structure of a graph and its behaviour with respect to hard problems [6]. Many NP-hard graph problems become solvable in polynomial time on graphs whose clique-width is bounded by a constant [21,26].…”

Section: Introductionmentioning

confidence: 99%

“…The disjoint union of G and H is the graph with vertex set V (G) ∪ V (H) and edge set E(G) ∪ E(H). The notion of clique-width was first introduced in [6]. The clique-width of a graph G is the minimum number of labels needed to construct G using the following four operations: create new vertex with label i, disjoint union, change all labels i to j, add all edges between vertices with label i and vertices with label j where i = j.…”

Section: Introductionmentioning

confidence: 99%

A Complete Characterisation of the Linear Clique-Width of Path Powers

Heggernes

Lecture Notes in Computer Science

Papadopoulos

2009

A k-path power is the k-power graph of a simple path of arbitrary length. Path powers form a non-trivial subclass of proper interval graphs. Their clique-width is not bounded by a constant, and no polynomial-time algorithm is known for computing their clique-width or linear clique-width. We show that k-path powers above a certain size have linear clique-width exactly k + 2, providing the first complete characterisation of the linear clique-width of a graph class of unbounded clique-width. Our characterisation results in a simple linear-time algorithm for computing the linear clique-width of all path powers.