منابع مشابه
On Hamiltonian Cycles through Prescribed Edges of a Planar Graph
We use [3] for terminology and notation not defined here and consider finite simple graphs only. The first major result on the existence of hamiltonian cycles in graphs embeddable in surfaces was by H. Whitney [12] in 1931, who proved that 4-connected maximal planar graphs are hamiltonian. In 1956, W.T. Tutte [10,11] generalized Whitney’s result from maximal planar graphs to arbitrary 4-connect...
متن کاملThe Hamiltonian path passing through prescribed edges in a star graph with faulty edges ∗
Let Fe be the set of faulty edges of Sn and E0 be the edge set of some pairwise vertex-disjoint paths of Sn. In [5], the authors showed that E0 lies on a Hamiltonian path P (u, v) of Sn−Fe where d(u, v) is odd, |Fe| ≤ n− 3, |E0| ≤ 2n− 7− 2|Fe|. In this paper we improve the previous result as follows: E0 lies on a Hamiltonian path P (u, v) of Sn − Fe where d(u, v) is odd, Fe ≤ n− 3, |E0| ≤ 2n− 6...
متن کاملCircuits in Graphs through a prescribed Set of Ordered vertices
A circuit in a simple undirected graphG = (V,E) is a sequence of vertices {v1, v2, . . . , vk+1} such that v1 = vk+1 and {vi, vi+1} ∈ E for i = 1, . . . , k. A circuit C is said to be edgesimple if no edge of G is used twice in C. In this article we study the following problem: which is the largest integer k such that, given any subset of k ordered vertices of a graph G, there exists an edge-si...
متن کاملPacking Directed Circuits through Prescribed Vertices Bounded Fractionally
A seminal result of Reed, Robertson, Seymour, and Thomas says that a directed graph has either k vertex-disjoint directed circuits or a set of at most f(k) vertices meeting all directed circuits. This paper aims at generalizing their result to packing directed circuits through prescribed vertices. Even, Naor, Schieber, and Sudan showed a fractional version of packing such circuits. In this pape...
متن کاملMatching extensions with prescribed and forbidden edges
Suppose G connected graph on p vertices that contains perfect Then G is said to have property n) if p 2: 2(m + n + 1) and if for each pair of disjoint independent M, N E( G) of m, n there exists a perfect matching P in G such that M S;;;; P and 0. We discuss the circumstances under which E(m, n) =? E(x, y), and prove that (surprisingly) in general E(m, n) does not imply E(m, n-1).
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ژورنال
عنوان ژورنال: Journal of Graph Theory
سال: 2019
ISSN: 0364-9024,1097-0118
DOI: 10.1002/jgt.22497