Back to Search
Start Over
Forbidden Subgraphs and Weak Locally Connected Graphs.
- Source :
-
Graphs & Combinatorics . Nov2018, Vol. 34 Issue 6, p1671-1690. 20p. - Publication Year :
- 2018
-
Abstract
- A graph is called H-free if it has no induced subgraph isomorphic to H. A graph is called Ni-locally connected if G[{x∈V(G):1≤dG(w,x)≤i}] is connected and N2-locally connected if G[{uv:{uw,vw}⊆E(G)}] is connected for every vertex w of G, respectively. In this paper, we prove the following.Every 2-connected P7-free graph of minimum degree at least three other than the Petersen graph has a spanning Eulerian subgraph. This implies that every H-free 3-connected graph (or connected N4-locally connected graph of minimum degree at least three) other than the Petersen graph is supereulerian if and only if H is an induced subgraph of P7, where Pi is a path of i vertices.Every 2-edge-connected H-free graph other than {K2,2k+1:kis a positive integer} is supereulerian if and only if H is an induced subgraph of P4.If every connected H-free N3-locally connected graph other than the Petersen graph of minimum degree at least three is supereulerian, then H is an induced subgraph of P7 or T2,2,3, i.e., the graph obtained by identifying exactly one end vertex of P3,P3,P4, respectively.If every 3-connected H-free N2-locally connected graph is hamiltonian, then H is an induced subgraph of K1,4. We present an algorithm to find a collapsible subgraph of a graph with girth 4 whose idea is used to prove our first conclusion above. Finally, we propose that the reverse of the last two items would be true. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 09110119
- Volume :
- 34
- Issue :
- 6
- Database :
- Academic Search Index
- Journal :
- Graphs & Combinatorics
- Publication Type :
- Academic Journal
- Accession number :
- 133270023
- Full Text :
- https://doi.org/10.1007/s00373-018-1952-2