Graph-Theoretic Concepts in Computer Science: 39th by Feodor F. Dragan (auth.), Andreas Brandstädt, Klaus Jansen,

By Feodor F. Dragan (auth.), Andreas Brandstädt, Klaus Jansen, Rüdiger Reischuk (eds.)

This publication constitutes the completely refereed complaints of the thirty ninth overseas Workshop on Graph Theoretic options in laptop technological know-how, WG 2013, held in Lübeck, Germany, in June 2013. The 34 revised complete papers offered have been conscientiously reviewed and chosen from sixty one submissions. The booklet additionally comprises abstracts. The papers conceal quite a lot of issues in graph conception regarding machine technology, equivalent to structural graph idea with algorithmic or complexity functions; layout and research of sequential, parallel, randomized, parameterized and dispensed graph and community algorithms; computational complexity of graph and community difficulties; computational geometry; graph grammars, graph rewriting structures and graph modeling; graph drawing and layouts; random graphs and versions of the net and scale-free networks; and aid of those recommendations through compatible implementations and applications.

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Extra resources for Graph-Theoretic Concepts in Computer Science: 39th International Workshop, WG 2013, Lübeck, Germany, June 19-21, 2013, Revised Papers

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Pathwidth of circular-arc graphs. , M¨ uller, H. ) WG 2007. LNCS, vol. 4769, pp. 258–269. Springer, Heidelberg (2007) 32. : Minimal acyclic forbidden minors for the family of graphs with bounded path-width. Discrete Mathematics 127(1-3), 293– 304 (1994) Threshold-Coloring and Unit-Cube Contact Representation of Graphs Md. Jawaherul Alam1 , Steven Chaplick2 , Gaˇsper Fijavˇz3 , Michael Kaufmann4, Stephen G. Kobourov1, , and Sergey Pupyrev1,5 1 Department of Computer Science, University of Arizona, Tucson, AZ, USA Department of Applied Mathematics, Charles University, Prague, Czech Republic 3 Faculty of Computer and Information Science, University of Ljubljana, Slovenia Wilhelm-Schickhard-Institut f¨ur Informatik, Universit¨at T¨ubingen, T¨ubingen, Germany 5 Institute of Mathematics and Computer Science, Ural Federal University, Russia 2 4 Abstract.

The vertices in X ∪ V (T ) \ {x} are cleared, all vertices in NT (x) ∩ Y are occupied, exactly |B | cops occupy vertices of T , and the set NT (B ) ∩ Y is occupied by cops. Theorem 11. Any forest T satisfies pw(T ) ≤ lrw(T ). Proof. We may assume that T is a tree. Let v1 , . . , vn be a linear ordering of V (T ) witnessing k := lrw(T ). For i ∈ [n] let Xi := {v1 , . . , vi } and Yi := {vi+1 , . . , vn }, and let Mi be AT [Xi , Yi ]. We describe a strategy for k + 1 cops in the invisible robber and cops game.

It follows that the linear clique-width of forests is linear time computable. In [11] it is proved that the linear clique-width of a graph is at most its path-width plus 2. We prove that for forests containing a path of length three, this upper bound is also a lower bound. Let us recall the definition of linear clique-width [11,15,27]. Let k be a positive integer. A k-labeled graph is a pair (G, γ) where G is a graph and γ : V (G) → [k] is a mapping; we will also denote it by (V (G), E(G), γ). The k-labeled graph consisting of a single vertex labeled by i ∈ [k] is denoted by (i, γi ).

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