Universal graphs with a forbidden subgraph: Block path solidity
نویسندگان
چکیده
منابع مشابه
Universal graphs with a forbidden subgraph: Block path solidity
Let C be a finite connected graph for which there is a countable universal C-free graph, and whose tree of blocks is a path. Then the blocks of C are complete. This generalizes a result of Füredi and Komjáth, and fits naturally into a set of conjectures regarding the existence of countable C-free graphs, with C an arbitrary finite connected graph.
متن کاملForbidden subgraph characterization of extended star directed path graphs that are not rooted directed path graphs
An asteroidal triple in a graph is a set of three non-adjacent vertices such that for any two of them there exists a path between them that does not intersect the neighborhood of the third. An asteroidal quadruple is a set of four non-adjacent vertices such that any three of them is an asteroidal triple. In this paper, we study a subclass of directed path graph, the class of extended star direc...
متن کاملUniversal Graphs (with Forbidden Subgraphs)
The graph theoretic problem of identifying the finite sets C of constraint graphs for which there is a countable universal C-free graph is closely related to the problem of determining for which sets C the model companion T ∗ C of the theory of C-free graphs is א0-categorical, and this leads back to combinatorics. Little is known about these theories from any other perspective, such as stabilit...
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 کاملUniversal graphs with a forbidden subtree
The systematic investigation of countable universal graphs with “forbidden” subgraphs was initiated in [13], followed by [12]. If C is a finite connected graph, then a graph G is C-free if it contains no subgraph isomorphic to C. A countable C-free graph G is weakly universal if every countable C-free graph is isomorphic to a subgraph of G, and strongly universal if every such graph is isomorph...
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: Combinatorica
سال: 2015
ISSN: 0209-9683,1439-6912
DOI: 10.1007/s00493-014-3181-5