A characterization of P5-free graphs with a homeomorphically irreducible spanning tree
نویسندگان
چکیده
منابع مشابه
A characterization of P5-free graphs with a homeomorphically irreducible spanning tree
A spanning tree with no vertices of degree two is called a homeomorphically irreducible spanning tree (or a HIST ) of a graph. In [7], sets of forbidden subgraphs that imply the existence of a HIST in a connected graph of sufficiently large order were characterized. In this paper, we focus on characterizing connected P5-free graphs which have a HIST. As applications of our main result, we also ...
متن کاملHomeomorphically irreducible spanning trees
We show that if G is a graph such that every edge is in at least two triangles, then G contains a spanning tree with no vertex of degree 2 (a homeomorphically irreducible spanning tree). This result was originally asked in a question format by Albertson, Berman, Hutchinson, and Thomassen in 1979, and then conjectured to be true by Archdeacon in 2009. MSC2010 : 05C05, 05C75
متن کاملHomeomorphically Irreducible Spanning Trees in Locally Connected Graphs
A spanning tree T of a graph G is called a homeomorphically irreducible spanning tree (HIST) if T does not contain vertices of degree 2. A graph G is called locally connected if for every vertex v ∈ V (G), the subgraph induced by the neighborhood of v is connected. In this paper, we prove that every connected and locally connected graph with more than 3 vertices contains a HIST. Consequently, w...
متن کاملHomeomorphically Irreducible Spanning Trees, Halin Graphs, and Long Cycles in 3-connected Graphs with Bounded Maximum Degrees
A tree T with no vertex of degree 2 is called a homeomorphically irreducible tree (HIT) and if T is spanning in a graph, then T is called a homeomorphically irreducible spanning tree (HIST). Albertson, Berman, Hutchinson and Thomassen asked if every triangulation of at least 4 vertices has a HIST and if every connected graph with each edge in at least two triangles contains a HIST. These two qu...
متن کاملCounting unlabelled three-connected and homeomorphically irreducible two-connected graphs
A graph will be assumed to be finite and unoriented, with no loops or multiple edges; if multiple edges are to be allowed, the term multigraph will be used. A graph or multigraph. will be called k-connected if at least k vertices and their incident edges must be removed to disconnect it (a complete graph is considered to be k-connected for any k). A block (respectively, multiblock) is a 2-conne...
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: Discrete Applied Mathematics
سال: 2015
ISSN: 0166-218X
DOI: 10.1016/j.dam.2014.12.023