Subgraphs, Closures and Hamiltonicity
نویسندگان
چکیده
Closure theorems in hamiltonian graph theory are of the following type: Let G be a 2connected graph and let II, u be two distinct nonadjacent vertices of G. If condition c(u, u) holds, then G is hamiltonian if and only if G + MU is hamiltonian. We discuss several results of this type in which u and v are vertices of a subgraph H of G on four vertices and c(u, u) is a condition on the neighborhoods of the vertices of H (in G). We also discuss corresponding sufficient conditions for hamiltonicity of G.
منابع مشابه
Hamiltonicity of Topological Grid Graphs
In this paper we study connectivity and hamiltonicity properties of the topological grid graphs, which are a natural type of planar graphs associated with finite subgraphs of the usual square lattice graph of the plane. The main results are as follows. The shortness coefficient of the family of all topological grid graphs is at most 16/17. Every 3-connected topological grid graph is hamiltonian.
متن کاملOn the number of specific spanning subgraphs of the graphs G x Pn
This paper investigates the number of spanning subgraphs of the product of an arbitrary graph G with the path graphs Pn on n vertices that meet certain properties: connectivity, acyclicity, Hamiltonicity, and restrictions on degree. A general method is presented for constructing a recurrence equation R(n) for the graphs G Pn, giving the number of spanning subgraphs that satisfy a given combinat...
متن کاملRecent research in Graph Theory
A well-known and fundamental property of graphs is Hamiltonicity. A connected graph is Hamiltonian if it contains a spanning cycle. Determining if a graph is Hamiltonian is known as a NP-complete problem and no satisfactory characterization exists. Nevertheless, many sufficient conditions for Hamiltonicity were found, usually expressed in terms of degree, connectivity, density, toughness, indep...
متن کاملForbidden Subgraphs for Hamiltonicity of 3-Connected Claw-Free Graphs
In this paper, we consider forbidden subgraphs for hamiltonicity of 3-connected claw-free graphs. Let Zi be the graph obtaind from a triangle by attaching a path of length i to one of its vertices, and let Q∗ be the graph obtained from the Petersen graph by adding one pendant edge to each vertex. Lai et al. [J. Graph Theory 64 (2010), no. 1, 1-11] conjectured that every 3-connected {K1,3, Z9}-f...
متن کاملClaw-free graphs - A survey
In this paper we summarize known results on claw-free graphs. The paper is subdivided into the following chapters and sections: 1. Introduction 2. Paths, cycles, hamiltonicity a) Preliminaries b) Degree and neighborhood conditions c) Local connectivity conditions d) Further forbidden subgraphs e) Invariants f) Squares g) Regular graphs h) Other hamiltonicity related results and generalizations ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Discrete Applied Mathematics
دوره 51 شماره
صفحات -
تاریخ انتشار 1994