On a problem of R. Halin concerning infinite graphs
نویسندگان
چکیده
منابع مشابه
On a problem of R. Halin concerning infinite graphs II
For every countable, connected graph A containing no one-way infinite path the following is shown: Let G be an arbitrary graph which contains for every positive integer n a system of n disjoint graphs each isomorphic to a subdivision of A. Then G also contains infinitely many disjoint subgraphs each isomorphic to a subdivision of A. In addition, corrections of errors are given that occur unfort...
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For the Traveling Salesman Problem (TSP) on Halin graphs with three types of cost functions: sum, bottleneck and balanced and with arbitrary real edge costs we compute in polynomial time the persistency partition EAll, ESome, ENone of the edge set E, where: EAll = {e ∈ E, e belongs to all optimum solutions}, ENone = {e ∈ E, e does not belong to any optimum solution} and ESome = {e ∈ E, e belong...
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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 ...
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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...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1978
ISSN: 0012-365X
DOI: 10.1016/0012-365x(78)90181-4