Tree-width of hypergraphs and surface duality
نویسندگان
چکیده
منابع مشابه
Tree-width of hypergraphs and surface duality
In Graph Minors III, Robertson and Seymour write:“It seems that the tree-width of a planar graph and the tree-width of its geometric dual are approximately equal — indeed, we have convinced ourselves that they differ by at most one.” They never gave a proof of this. In this paper, we prove a generalisation of this statement to embedding of hypergraphs on general surfaces, and we prove that our ...
متن کاملTree-width of graphs and surface duality
In Graph Minors III, Robertson and Seymour conjecture that the tree-width of a graph and that of its dual differ by at most one. In this paper, we prove that given a hypergraph H on a surface of Euler genus k, the tree-width of H∗ is at most the maximum of tw(H) + 1 + k and the maximum size of a hyperedge of H∗ minus one.
متن کاملThe Tree-Width Compactness Theorem for Hypergraphs
A hypergraph H has tree-width k (a notion introduced by Robertson and Seymour) if k is the least integer such that H admits a tree-decomposition of tree-width k. We prove a compactness theorem for this notion, that is, if every finite subhypergraph of H has tree-width < k, then H itself has tree-width < k. This result will be used in a later paper on well-quasi-ordering infinite graphs.
متن کاملSubset Glauber Dynamics on Graphs, Hypergraphs and Matroids of Bounded Tree-Width
Motivated by the ‘subgraphs world’ view of the ferromagnetic Ising model, we analyse the mixing times of Glauber dynamics based on subset expansion expressions for classes of graph, hypergraph and matroid polynomials. With a canonical paths argument, we demonstrate that the chains defined within this framework mix rapidly upon graphs, hypergraphs and matroids of bounded tree-width. This extends...
متن کاملTree-Width and Dimension
Over the last 30 years, researchers have investigated connections between dimension for posets and planarity for graphs. Here we extend this line of research to the structural graph theory parameter tree-width by proving that the dimension of a finite poset is bounded in terms of its height and the tree-width of its cover graph.
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: 2012
ISSN: 0095-8956
DOI: 10.1016/j.jctb.2011.11.002