Spanning trees with many leaves
WebSpanning trees with many leaves: new lower bounds in terms of number of vertices of degree 3 and at least 4 D.V.Karpov E-mail: [email protected] Abstract We prove, that every connected graph with svertices of degree 3 and t vertices of degree at least 4 has a spanning tree with at least 2 5 t+ 1 5 s+ leaves, where 8 5 Web10. júl 2001 · Spanning trees with many leaves. Guoli Ding, Department of Mathematics, Louisiana State University, Baton Rouge, La 70803. Search for more papers by this author. …
Spanning trees with many leaves
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Web24. mar 2024 · A spanning tree of a graph on n vertices is a subset of n-1 edges that form a tree (Skiena 1990, p. 227). For example, the spanning trees of the cycle graph C_4, diamond graph, and complete graph K_4 are … Web29. jan 1999 · In the Maximum Leaf Spanning Tree problem, one is given a connected undirected graph G and wants to find a spanning tree of G with the maximum number of leaves, where a leaf is a...
Web25. jún 2024 · Since spanning trees form a matroid, one can indeed transform a spanning tree into any other via a sequence of edge flips, as observed by Ito et al. We investigate the problem of determining, given two spanning trees T_1,T_2 with an additional property Π, if there exists an edge flip transformation from T_1 to T_2 keeping property Π all along. Web18. júl 2007 · Spanning Trees with Many Leaves in Graphs without Diamonds and Blossoms Paul Bonsma, Florian Zickfeld It is known that graphs on n vertices with minimum degree at least 3 have spanning trees with at least n/4+2 leaves and that this can be improved to (n+4)/3 for cubic graphs without the diamond K_4-e as a subgraph.
WebThe Directed Maximum Leaf Out-Branching problem is to find an out-branching (i.e., a rooted oriented spanning tree) in a given digraph with the maximum number of leaves. In this …
WebFor a connected graph G let L(G) denote the maximum number of leaves in any spanning tree of G. We give a simple construction and a complete proof of a result of Storer that if G is a connected cubic graph on n vertices, then L(G) ⩾ [(n/4) + 2], and this is best possible for all (even) n. The main idea is to count the number of “dead leaves” as the tree is being …
Web11. feb 2008 · Bill Waller Abstract and Figures In this paper we prove several new lower bounds on the maximum number of leaves of a spanning tree of a graph related to its … henry kearneyWeb1. dec 2011 · Spanning trees with many leaves Authors: D. V. Karpov Abstract Let a maximal chain of vertices of degree 2 in a graph G consist of k > 0 vertices. We prove that G has a … henry k carroll puerto ricoWeb3. okt 2024 · As Gis connected, there is a spanning tree Tin G. By our hypothesis, i.e., Gdoes not contain a spanning 6-ended tree, the number of leaves in Tis at least 7. If the number of leaves in Tis 7, then we have found a tree with exactly 7 leaves. henry k claiborneWebCiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): A connected graph having large minimum vertex degree must have a spanning tree with many leaves. In particular, let l(n, k) be the maximum integer m such that every connected n-vertex graph with minimum degree at least k has a spanning tree with at least m leaves. Then l(n, 3) ≥ … henryk cymermanWebWe consider the problem of finding a spanning tree that maximizes the number of leaves (MaxLeaf). We provide a 3/2-approximation algorithm for this problem when restricted to cubic graphs, improving on the previous 5/3-approximation for this class. henryk cnotaWeb1. aug 2001 · Note that finding the maximum number of leaves in a spanning tree of G is NPhard . Linial and Sturtevant (unpublished) [12] proved that ℓ (n, 3) ≥ n/4 + 2. For δ = 4, … henry kearse syracuse nyWeb1. jan 2016 · The Max Leaf Spanning Tree problem asks us to find a spanning tree with at least k leaves in an undirected graph. The decision version of parameterized Max Leaf Spanning Tree is the following: MAX LEAF SPANNING TREE Input: A connected graph G, and an integer k. Parameter: An integer k. Question: Does G have a spanning tree with at … henry kearney robersonville nc