Bounding Tree-Width via Contraction on the Projective Plane and Torus.
نویسندگان
چکیده
منابع مشابه
Bounding Tree-Width via Contraction on the Projective Plane and Torus
If X is a collection of edges in a graph G, let G/X denote the contraction of X. Following a question of Oxley and a conjecture of Oporowski, we prove that every projective-planar graph G admits an edge-partition {X,Y } such that G/X and G/Y have tree-width at most three. We prove that every toroidal graph G admits an edge-partition {X,Y } such that G/X and G/Y have tree-width at most three and...
متن کاملBounding connected tree-width
Diestel and Müller showed that the connected tree-width of a graph G, i. e., the minimum width of any tree-decomposition with connected parts, can be bounded in terms of the tree-width of G and the largest length of a geodesic cycle in G. We improve their bound to one that is of correct order of magnitude. Finally, we construct a graph whose connected tree-width exceeds the connected order of a...
متن کاملBounding Clique-Width via Perfect Graphs
Given two graphs H1 and H2, a graph G is (H1,H2)-free if it contains no subgraph isomorphic to H1 or H2. We continue a recent study into the clique-width of (H1,H2)-free graphs and present three new classes of (H1, H2)-free graphs that have bounded clique-width. We also show the implications of our results for the computational complexity of the Colouring problem restricted to (H1,H2)-free grap...
متن کاملPercolation on the Projective Plane
Since the projective plane is closed, the natural homological observable of a percolation process is the presence of the essential cycle in H1(RP 2; Z2). In the Voroni model at critical phase, pc = .5, this observable has probability q = .5 independent of the metric on RP 2. This establishes a single instance (RP 2, homological observable) of a very general conjecture about the conformal invari...
متن کاملConics on the Projective Plane
In this paper, we discuss a special property of conics on the projective plane and answer questions in enumerative algebraic geometry such as ”How many points determine a conic?” and ”How many conics do we expect to pass through m points and tangent to n lines?”
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: The Electronic Journal of Combinatorics
سال: 2015
ISSN: 1077-8926
DOI: 10.37236/2534