Tree-depth, subgraph coloring and homomorphism bounds
نویسندگان
چکیده
منابع مشابه
Tree-depth, subgraph coloring and homomorphism bounds
We define the notions tree-depth and upper chromatic number of a graph and show their relevance to local–global problems for graph partitions. In particular we show that the upper chromatic number coincides with the maximal function which can be locally demanded in a bounded coloring of any proper minor closed class of graphs. The rich interplay of these notions is applied to a solution of boun...
متن کاملTight Bounds for Graph Homomorphism and Subgraph Isomorphism
We prove that unless Exponential Time Hypothesis (ETH) fails, deciding if there is a homomorphism from graph G to graph H cannot be done in time |V (H)|o(|V (G)|). We also show an exponential-time reduction from Graph Homomorphism to Subgraph Isomorphism. This rules out (subject to ETH) a possibility of |V (H)|o(|V (H)|)-time algorithm deciding if graph G is a subgraph of H. For both problems o...
متن کاملTight Bounds for Subgraph Isomorphism and Graph Homomorphism
We prove that unless Exponential Time Hypothesis (ETH) fails, deciding if there is a homomorphism from graph G to graph H cannot be done in time |V (H)|o(|V . Combined with the reduction of Cygan, Pachocki, and Soca la, our result rules out (subject to ETH) a possibility of |V (G)|o(|V -time algorithm deciding if graph H is a subgraph of G. For both problems our lower bounds asymptotically matc...
متن کاملQuantum Query Complexity of Subgraph Isomorphism and Homomorphism
Let H be a fixed graph on n vertices. Let fH(G) = 1 iff the input graph G on n vertices contains H as a (not necessarily induced) subgraph. Let αH denote the cardinality of a maximum independent set of H. In this paper we show: Q(fH) = Ω ( √ αH · n) , where Q(fH) denotes the quantum query complexity of fH . As a consequence we obtain a lower bounds for Q(fH) in terms of several other parameters...
متن کاملColoring Graphs Characterized by a Forbidden Subgraph
The Coloring problem is to test whether a given graph can be colored with at most k colors for some given k, such that no two adjacent vertices receive the same color. The complexity of this problem on graphs that do not contain some graph H as an induced subgraph is known for each fixed graph H. A natural variant is to forbid a graph H only as a subgraph. We call such graphs strongly H-free an...
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: European Journal of Combinatorics
سال: 2006
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2005.01.010