Given a 3-connected planar graph G with n vertices, is there a spanning closed walk W with at most 4n/3 edges? In graph theory, the above question is motivated by the famous hamiltonian result by Tutte in 1956 which says that every 4-connected planar graph is hamiltonian (a simpler ...
adjective (graph theory, of a walk) Whose first and last vertices are the same. verb simple past tense and past participle of [i]close[/i] Pertaining to the status of an opportunity where all sales stages are complete and no further activity is required. Inaccessible. closed (e.g...
Definition 3.5 In a graph G, a circuit is a closed walk. Definition 3.6 Let (u,v) be an edge of a directed tripartite graph G. L(v)={u|(u,v)∈E} denotes the set of all adjacent nodes of the vertex v lying to the left of it. In an analogous way, R(u)={v|(u,v)∈E...
of Fundamental Physics-Marco Drewes 1:05:59 国际基础科学大会-String Theory and Geometric Representation Theory-Philsang Yoo 1:01:44 国际基础科学大会-Gromov-Witten type theory and statistical physics-Jian Zhou 59:52 国际基础科学大会-Random walk on dynamical percolation: separating critical and... ...
Thus W′ is a spanning walk in H. Therefore H is connected, as claimed. Let H′ be the subgraph of H formed by the dual-half-chords of T. We now show that H′ is 2-regular. Consider a dual-half-chord fg of T. Let vw be the corresponding half-chord of G, where v∈V(T) ...
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That is the same as saying that d3 (S) is the length of the shortest closed walk through the vertices {x1, . . . , xk}. Recall that the Steiner distance sd(S) is the number of edges in a minimum connected subgraph containing all of the vertices of S. We note some relationships ...
A Hamiltonian walk of a graph is a closed spanning walk of minimum length. In this paper we generalize a Dirac type sufficient condition ensuring the existence of a Hamiltonian cycle to one ensuring the existence of a closed spanning walk of length less than a specified value. Furthermore, ...
Closed walk3-connected planar graphsTSPHeld-Karp relaxationIntegrality gap4/3-conjectureIn this paper, we prove the following theorem, which is motivated by two different contexts independently, namely graph theory and combinatorial optimization.
simple alternating walk argument shows that integral vectors in the alternating cone are sums of characteristic vectors of closed alternating walks (thereby justifying our terminology). In the paper =-=[BPS1]-=- alternating walk arguments are used to study basic properties of the alternating cone ...