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Mathematical tree with cycle through leaves
In graph theory, a Halin graph is a type of planar graph, constructed by connecting the leaves of a tree into a cycle. The tree must have at least four
Halin_graph
Graph that can be embedded in the plane
a polyhedral graph in which one face is adjacent to all the others. Every Halin graph is planar. Like outerplanar graphs, Halin graphs have low treewidth
Planar_graph
Cubic graph with 12 vertices and 18 edges
Frucht graph provides an example of this strengthened realization for the trivial group. The Frucht graph is a Halin graph, a type of planar graph formed
Frucht_graph
Graph containing cycles of all possible lengths
{\displaystyle k} , it has cycles of all smaller lengths. Halin graphs are the planar graphs formed from a planar drawing of a tree that has no degree-two
Pancyclic_graph
Cycle graph plus universal vertex
every wheel graph is a Halin graph. They are self-dual: the planar dual of any wheel graph is an isomorphic graph. Every maximal planar graph, other than
Wheel_graph
German mathematician
Rudolf Halin (February 3, 1934 – November 14, 2014) was a German graph theorist, known for defining the ends of infinite graphs, for Halin's grid theorem
Rudolf_Halin
Non-crossing graph with vertices on outer face
planar dual of a Halin graph is an outerplanar graph. A planar graph is outerplanar if and only if its weak dual is a forest, and it is Halin if and only if
Outerplanar_graph
Prism with a 3-sided base
type of planar graph formed from a tree with no degree-two vertices by adding a cycle connecting its leaves, an example of Halin graph. When all edges
Triangular_prism
Decomposition of a graph into hamiltonion cycles
3-regular graph is planar and bipartite, when it is a Halin graph, when it is itself a prism or Möbius ladder, or when it is a generalized Petersen graph of
Hamiltonian_decomposition
Graph made from vertices and edges of a convex polyhedron
simple; the tetrahedral, octahedral, and icosahedral graphs are simplicial. The Halin graphs, graphs formed from a planar embedded tree by adding an outer
Polyhedral_graph
Theorem about infinite graphs
In graph theory, a branch of mathematics, Halin's grid theorem states that the infinite graphs with thick ends are exactly the graphs containing subdivisions
Halin's_grid_theorem
Special labeling in graph theory
proved that if G is a Halin graph with ∆(G) > 4 then χ i ( G ) = Δ ( G ) + 1. {\displaystyle \chi _{i}(G)=\Delta (G)+1.} For Halin graphs with ∆(G) = 3 or
Incidence_coloring
one end. Ends of graphs were defined by Rudolf Halin (1964) in terms of equivalence classes of infinite paths. A ray in an infinite graph is a semi-infinite
End_(graph_theory)
Number denoting a graph's closeness to a tree
the cactus graphs, pseudoforests, series–parallel graphs, outerplanar graphs, Halin graphs, and Apollonian networks. The control-flow graphs arising in
Treewidth
Subgraph of planar graph with Hamiltonian cycle
include the 4-connected planar graphs, by Tutte's theorem on Hamiltonian cycles, and the Halin graphs. Every planar graph with maximum degree at most four
Subhamiltonian_graph
Mapping of a graph into a tree
A16:1–A16:35, doi:10.1145/2220357.2220363, MR 2946220 Halin, Rudolf (1976), "S-functions for graphs", Journal of Geometry, 8 (1–2): 171–186, doi:10.1007/BF01917434
Tree_decomposition
Method in geometry for representing a polygon by a topological skeleton
corresponding to this straight skeleton forms a Steinitz realization of the Halin graph formed from the tree by connecting its leaves in a cycle. Barequet et
Straight_skeleton
On linear-time algorithms for graph logic
k-outerplanar graphs. The general version of the conjecture was finally proved by Mikołaj Bojańczyk and Michał Pilipczuk. Moreover, for Halin graphs (a special
Courcelle's_theorem
Families of graphs with this property include the cactus graphs, pseudoforests, series–parallel graphs, outerplanar graphs, Halin graphs, and Apollonian
Partial_k-tree
Size of largest complete graph made by contracting edges of a given graph
the graph. Every graph with Hadwiger number k has at most n2O(k log(log k)) cliques (complete subgraphs). Halin (1976) defines a class of graph parameters
Hadwiger_number
Tree graph with all nodes within distance 1 from central path
time algorithms if a graph is an outerplanar, a series-parallel, or a Halin graph. Caterpillar trees have been used in chemical graph theory to represent
Caterpillar_tree
Theorem in graph theory
infinite graphs, and in that context it applies to the minimum cut between any two elements that are either vertices or ends of the graph (Halin 1974).
Menger's_theorem
Graph-theoretic description of polyhedra
configuration) that have no integer equivalent. A Halin graph is a special case of a polyhedral graph, formed from a planar-embedded tree (with no degree-two
Steinitz's_theorem
given finite graph is equal to the maximal value of k {\displaystyle k} for which the graph contains a k {\displaystyle k} -skein. Halin, R. (1997)
Skein_(graph_theory)
Numerical invariant of graphs
outerplanar graphs, series–parallel graphs, and Halin graphs all have bounded treewidth, they all also have at most logarithmic tree-depth. The typical graphs with
Tree-depth
Representation of a graph as a path graph "thickened" by some amount
polynomial time for graphs of bounded treewidth including series–parallel graphs, outerplanar graphs, and Halin graphs, as well as for split graphs, for the complements
Pathwidth
97, English Battle of Britain fighter pilot. Rudolf Halin, 80, German graph theorist (Halin graph). Francis Harvey, 89, Irish poet. Kajetan Kovič, 83
Deaths_in_November_2014
British church minister and mathematician (1806–1895)
on the Icosian game. He enumerated cubic Halin graphs, over a century before the work of Halin on these graphs. He showed that every polyhedron can be
Thomas_Kirkman
British Othello player (born 1963)
included the proof, with Reinhard Diestel, of the bounded graph conjecture of Rudolf Halin. Leader in an interview in 2016 stated that he began to play
Imre_Leader
Israeli mathematician and computer scientist
these two graph properties is a key component of the Robertson–Seymour theorem, is closely related to Halin's grid theorem for infinite graphs, and underlies
Julia_Chuzhoy
Type of total coloring in graph theory
Chen, Xiang-en; Zhang, Zhong-fu (2008). "AVDTC numbers of generalized Halin graphs with maximum degree at least 6". Acta Mathematicae Applicatae Sinica
Adjacent-vertex-distinguishing-total coloring
Adjacent-vertex-distinguishing-total_coloring
fixed h-vertex apex graph as a minor and of treewidth at least g(h) r can be edge-contracted to Γ r {\displaystyle \Gamma _{r}} . Halin's grid theorem is
Bidimensionality
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