WebForm n graphrs, fo Gr r = 1, 2, . . . , n, from the graph of Figure 1 by inserting the graphn(x) H of Figure 4 in each of the faces labeled H(x) for x = dzu, zkv, dtw. Each of the resulting graphs is clearly 5'-embeddable and has 6n vertices. Other than the dual base verticesn(x) ha, thse n graph H vertices. WebJun 22, 1999 · In this article, we show that every simple r -regular graph G admits a balanced P4 -decomposition if r ≡ 0 (mod 3) and G has no cut-edge when r is odd. We also …
Hamilton Decomposition -- from Wolfram MathWorld
WebThe definition is sometimes extended to a decomposition into Hamiltonian cycles for a regular graph of even degree or into Hamiltonian cycles and a single perfect matching for a regular graph of odd degree (Alspach 2010), with a decomposition of the latter type being known as a quasi-Hamilton decomposition (Bosák 1990, p. 123). Webregular graphs. 2.1. Strongly regular graphs and restricted eigenvalues A strongly regular graph G with parameters (v,k,λ,µ) is a non-complete graph on v vertices which is regular with valency k, and which has the property that any two adjacent vertices have λ common neighbours, and any two non-adjacent vertices have µ common neighbours. pop regular arriving flights may 4th
arXiv:1503.00494v2 [math.CO] 20 Jun 2016
Webthe end vertices of each path are in Y. As a consequence, every 6-regular bipartite graph on n vertices can be decomposed into n 2 paths, all of which have the same length 6. This verifies Conjecture 1.3 for 6-regular bipartite graphs. To obtain P 6-decompositions of 6-regular bipartite graphs, we first show that there is a WebThe following theorem summarises our optimal decomposition results for dense random graphs. We denote by odd(G) the number of odd degree vertices in a graph G. Theorem 1.2. Let 0 < p < 1 be constant and let G ∼ Gn,p. Then a.a.s. the following hold: (i) G can be decomposed into ⌊∆(G)/2⌋ cycles and a matching of size odd(G)/2. WebRegular clique covers of graphs, Australas. J. Combin., 27, 2003, pp. 307–316. 35. (with. Z. Ryjáček and Z. Skupień) On traceability and 2-factors in claw-free graphs, Discussiones Mathematicae Graph Theory, 24 (2004), 55–71. 36. Cyclic decompositions of complete graphs into spanning trees, Discussiones Mathematicae Graph Theory, 24 sharing purchased books on kindle