Vertex-minor reductions can simulate edge contractions
نویسندگان
چکیده
منابع مشابه
Vertex-minor reductions can simulate edge contractions
We prove that local complementation and vertex deletion, operations from which vertexminors are defined, can simulate edge contractions. As an application, we prove that the rank-width of a graph is linearly bounded in term of its tree-width.
متن کاملEdge-coloring Vertex-weightings of Graphs
Let $G=(V(G),E(G))$ be a simple, finite and undirected graph of order $n$. A $k$-vertex weightings of a graph $G$ is a mapping $w: V(G) to {1, ldots, k}$. A $k$-vertex weighting induces an edge labeling $f_w: E(G) to N$ such that $f_w(uv)=w(u)+w(v)$. Such a labeling is called an {it edge-coloring k-vertex weightings} if $f_{w}(e)not= f_{w}(echr(chr(chr('39')39chr('39'))39chr(chr('39')39chr('39'...
متن کاملVertex Sparsification and Oblivious Reductions
Given an undirected, capacitated graph G = (V,E) and a set K ⊂ V of terminals of size k, we construct an undirected, capacitated graph G′ = (K,E′) for which the cut-function approximates the value of every minimum cut separating any subset U of terminals from the remaining terminals K −U . We refer to this graph G′ as a cut-sparsifier, and we prove that there are cut-sparsifiers that can approx...
متن کاملOn Vertex, Edge, and Vertex-Edge Random Graphs (Extended Abstract)
We consider three classes of random graphs: edge random graphs, vertex random graphs, and vertex-edge random graphs. Edge random graphs are Erdős-Rényi random graphs [9, 10], vertex random graphs are generalizations of geometric random graphs [21], and vertex-edge random graphs generalize both. The names of these three types of random graphs describe where the randomness in the models lies: in ...
متن کاملOn Vertex, Edge, and Vertex-edge Random Graphs
We consider three classes of random graphs: edge random graphs, vertex random graphs, and vertex-edge random graphs. Edge random graphs are Erdős-Rényi random graphs [8, 9], vertex random graphs are generalizations of geometric random graphs [20], and vertexedge random graphs generalize both. The names of these three types of random graphs describe where the randomness in the models lies: in th...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2007
ISSN: 0166-218X
DOI: 10.1016/j.dam.2007.06.011