منابع مشابه
Boxicity of Halin graphs
A k-dimensional box is the Cartesian product R1 × R2 × · · · ×Rk where each Ri is a closed interval on the real line. The boxicity of a graph G, denoted as box(G) is the minimum integer k such that G is the intersection graph of a collection of k-dimensional boxes. Halin graphs are the graphs formed by taking a tree with no degree 2 vertex and then connecting its leaves to form a cycle in such ...
متن کاملLovász-Plummer conjecture on Halin graphs
A Halin graph, defined by Halin [3], is a plane graph H = T ∪ C such that T is a spanning tree of H with no vertices of degree 2 where |T | ≥ 4 and C is a cycle whose vertex set is the set of leaves of T . In his work, as an example of a class of edge-minimal 3-connected plane graphs, Halin constructed this family of plane graphs, which have many interesting properties. Lovász and Plummer [5] n...
متن کاملDominating cycles in halin graphs
A cycle in a graph is dominating if every vertex lies at distance at most one from the cycle and a cycle is D-cycle if every edge is incident with a vertex of the cycle. In this paper, first we provide recursive formulae for finding a shortest dominating cycle in a Hahn graph; minor modifications can give formulae for finding a shortest D-cycle. Then, dominating cycles and D-cycles in a Halin g...
متن کاملSome Combinatorial Problems on Halin Graphs
Let T be a tree with no degree 2 vertices and L(T) = {l1,. .. , lr}, r ≥ 2 denote the set of leaves in T. An Halin graph G is a graph obtained from T such that V (G) = V (T) and E(G) = E(T) ∪ {{li, li+1} | 1 ≤ i ≤ r − 1} ∪ {l1, lr}. In this paper, we investigate combinatorial problems such as, testing whether a given graph is Halin or not, chromatic bounds, an algorithm to color Halin graphs wi...
متن کاملOn orienting graphs for connectivity: Projective planes and Halin graphs
Nash-Williams proved that the edges of a k-edge connected (undirected) graph can be oriented such that the resulting directed graph is ⌊ 2 ⌋-edge connected. A long-standing goal in the area is to obtain analogous results for other types of connectivity, such as node connectivity, element connectivity, and hypergraph edge connectivity. We focus on two special classes of graphs, namely, incidence...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1983
ISSN: 0012-365X
DOI: 10.1016/0012-365x(83)90094-8