Small graph classes and bounded expansion
نویسندگان
چکیده
منابع مشابه
Small graph classes and bounded expansion
A class of simple undirected graphs is small if it contains at most n!α labelled graphs with n vertices, for some constant α. We prove that for any constants c, ε > 0, the class of graphs with expansion bounded by the function f(r) = c 1/3−ε is small. Also, we show that the class of graphs with expansion bounded by 6 · 3 √ r log(r+e) is not small. We work with simple undirected graphs, without ...
متن کاملCharacterisations and examples of graph classes with bounded expansion
Classes with bounded expansion, which generalise classes that exclude a topological minor, have recently been introduced by Nešetřil and Ossona de Mendez. These classes are defined by the fact that the maximum average degree of a shallow minor of a graph in the class is bounded by a function of the depth of the shallow minor. Several linear-time algorithms are known for bounded expansion classe...
متن کاملDistributed Domination on Graph Classes of Bounded Expansion
We provide a new constant factor approximation algorithm for the (connected) distance-r dominating set problem on graph classes of bounded expansion. Classes of bounded expansion include many familiar classes of sparse graphs such as planar graphs and graphs with excluded (topological) minors, and notably, these classes form the most general subgraph closed classes of graphs for which a sequent...
متن کاملGrad and classes with bounded expansion III. Restricted graph homomorphism dualities
We study restricted homomorphism dualities in the context of classes with bounded expansion. This presents a generalization of restricted dualities obtained earlier for bounded degree graphs and also for proper minor closed classes. This is related to distance coloring of graphs and to the “approximative version” of Hadwiger conjecture.
متن کاملGrad and classes with bounded expansion I. Decompositions
We introduce classes of graphs with bounded expansion as a generalization of both proper minor closed classes and degree bounded classes. Such classes are based on a new invariant, the greatest reduced average density (grad) of G with rank r, ∇r(G). For these classes we prove the existence of several partition results such as the existence of low tree-width and low tree-depth colorings. This ge...
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: Journal of Combinatorial Theory, Series B
سال: 2010
ISSN: 0095-8956
DOI: 10.1016/j.jctb.2009.06.001