Alternating diagrams of 4-regular graphs in 3-space
نویسندگان
چکیده
منابع مشابه
Some 3 - regular 4 - ordered graphs ∗
A graph G is k-ordered if for any sequence of k distinct vertices v1, v2, . . . , vk of G there exists a cycle in G containing these k vertices in the specified order. In 1997, Ng and Schultz posed the question of the existence of 3-regular 4-ordered graphs other than K4 and K3,3. In 2008, Meszaros solve the question by proving the Petersen graph and the Heawood graph are 3-regular 4-ordered gr...
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A simple graph G is k-ordered (respectively, k-ordered hamiltonian), if for any sequence of k distinct vertices v1, . . . , vk of G there exists a cycle (respectively, hamiltonian cycle) in G containing these k vertices in the specified order. In 1997 Ng and Schultz introduced these concepts of cycle orderability and posed the question of the existence of 3-regular 4-ordered (hamiltonian) graph...
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A graph G is k-ordered if for any sequence of k distinct vertices v1, v2, . . . , vk of G there exists a cycle in G containing these k vertices in the specified order. In 1997, Ng and Schultz posed the question of the existence of 4-ordered 3-regular graphs other than the complete graph K4 and the complete bipartite graph K3,3. In 2008, Meszaros solved the question by proving that the Petersen ...
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Let denote a bipartite distance-regular graph with diameter D ≥ 3 and valency k ≥ 3. Let θ0 > θ1 > · · · > θD denote the eigenvalues of and let qh i j (0 ≤ h, i, j ≤ D) denote the Krein parameters of . Pick an integer h (1 ≤ h ≤ D − 1). The representation diagram = h is an undirected graph with vertices 0, 1, . . . , D. For 0 ≤ i, j ≤ D, vertices i, j are adjacent in whenever i = j and qh i j =...
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We show that a random 4-regular graph asymptotically almost surely (a.a.s.) has chromatic number 3. The proof uses an efficient algorithm which a.a.s. 3colours a random 4-regular graph. The analysis includes use of the differential equation method, and exponential bounds on the tail of random variables associated with branching processes. A substantial part of the analysis applies to random d-r...
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 1999
ISSN: 0166-8641
DOI: 10.1016/s0166-8641(97)00268-x