Geometric Thickness of Complete Graphs
Geometric Thickness of Complete Graphs
... 101 for h ≥ This completes the proof of Theorem 4.1 Geometric Thickness of Complete Bipartite Graphs In this section we consider the geometric thickness of complete bipartite graphs, Ka,b We ... bipartite graphs with arbitrarily many vertices for which the standard thickness and geometric thickness coincide We also show that the bounds on geometric thickness of complete bipartite graphs ... problems motivate the subject of this paper, namely the geometric thickness of a graph We define θ(G), the geometric thickness of a graph G, to be the smallest value of k such that we can assign...
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Báo cáo toán học: "k-cycle free one-factorizations of complete graphs" pptx
... in a given one-factorization of Kn The next infinite class of one-factorizations yields further examples of k-cycle free and k < -cycle free one-factorizations of complete graphs Construction ... k-cycle free one-factorization of Kn+1 , then a k-cycle free one-factorization of Kpn+1 exists ˜ Proof: Assume that a k-cycle free one-factorization F of Kn+1 is given Let H be the union of two ... k-cycle free one-factorization of Kn+1 , then a k-cycle free one-factorization of Kpn+1 exists ˜ Proof: Assume that a k-cycle free one-factorization F of Kn is given Let H be the union of two...
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Báo cáo toán học: "On a theorem of Erd˝s, Rubin, and Taylor on o choosability of complete bipartite graphs" pptx
... Erd˝s, Rubin, and Taylor) o A vertex t-coloring of a hypergraph H is panchromatic if each of the t colors is used on every edge of G Thus, an ordinary 2-coloring is panchromatic Some results on the ... R Woodall, Density conditions for panchromatic colourings of hypergraphs, Combinatorica, 21 (2001), 515–541, [9] J Radhakrishnan and A Srinivasan, Improved bounds and algorithms for hypergraph ... and Finite Sets, A Hajnal et al., editors, Colloq Math Soc J Bolyai, 11, North Holland, Amsterdam, 609–627, 1975 [6] P Erd˝s, A. L Rubin and H Taylor, Choosability in graphs, Proc West Coast o...
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Báo cáo toán học: "The Directed Anti-Oberwolfach Solution: Pancyclic 2-factorizations of complete directed graphs of odd order" doc
... class of 2-factorizations The undirected anti-Oberwolfach question has been solved affirmatively for all complete graphs of odd order, complete graphs of even order with a 1-factor removed and all complete ... range of directed 2-factorization problems we have solved the directed pancyclic 2-factorization for all directed complete graphs of odd order except K5 which we prove has no directed pancyclic ... complete bipartite graphs [7] We show here that all directed complete graphs of odd order have a directed anti-Oberwolfach decomposition The solution method is a combination of Piotrowski’s approach...
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Báo cáo toán học: "Bounded-Degree Graphs have Arbitrarily Large Geometric Thickness" potx
... arbitrarily large geometric thickness In particular, for all ∆ ≥ and for all large √ n, there exists a ∆-regular graph with geometric thickness at least c ∆ n1/2−4/∆− ... graphs: a survey Graphs Combin., 14(1):59–73, 1998 the electronic journal of combinatorics 13 (2006), #R3 12 ´ ¨ ¨ ¨ ´ ¨ [24] Janos Pach and Domotor Palvolgyi Bounded-degree graphs can have arbitrarily ... tight Duncan et al [11] proved that the y geometric thickness of a degree-4 graph is at most Eppstein [13] asked whether graphs of bounded degree have bounded geometric thickness The first contribution...
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Báo cáo toán học: "Jamming and geometric representations of graphs" ppsx
... simplification of G and let F be a flat face of G We know that it is a subdivision of C2 , and each edge of F belongs to one of the two sides of C2 Lemma Let e be an edge of G and let l be the ... sides of a flat face of G Proof This is a corollary of Lemma The notion of the pseudo–embedding may be extended to the representations of a graph on the sphere and to the proper toroidal representations ... electronic journal of combinatorics 13 (2006), #R56 i.e the representations of the vertices are all different and the interiors of the representations of the edges are disjoint and not contain a...
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Báo cáo toán học: "The IC-Indices of Complete Bipartite Graphs" potx
... several properties of a maximal IC-coloring f of Km,n Proposition 3.3 If f is a maximal IC-coloring of G = (A, B) = Km,n , then all the colorings of vertices of G are distinct Proof Suppose, to ... ) Hence, we have a contradiction and the proof is complete the electronic journal of combinatorics 15 (2008), #R43 Lemma 2.4 Let f be an IC-coloring of a graph G such that f (ui ) < f (ui+1 ) ... = φ Therefore, the number of induced connected subgraphs of Km,n is equal to (m + n) + (2m − 1)(2n − 1) Note that the number of distinct induced connected subgraphs of G does provide a natural...
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Báo cáo toán học: "Some gregarious cycle decompositions of complete equipartite graphs" ppsx
... “nongregarious” cycle decompositions, few results are known Of course 3 -cycle decompositions of complete equipartite graphs are necessarily gregarious and so by Hanani [5], the electronic journal of combinatorics ... section we introduce some new techniques for obtaining gregarious cycle decompositions of complete equipartite graphs from cycle decompositions of related multigraphs The techniques used are similar ... pairs of cycles in such a way that the cycles in each pair share two adjacent edges Then there exists a gregarious k -cycle decomposition of G ∗ K Proof Let D be a k -cycle decomposition of 2G...
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Báo cáo toán học: "Sharply transitive 1-factorizations of complete multipartite graphs" pot
... proof of this last statement is quite simple, see Lemma 2.1 of [7] or Proposition 2.2 of [10] for instance In this paper we focus our attention on complete multipartite graphs We denote a complete ... In this manner we complete Σ′ to a starter for (G, Ω) Sharply transitive 1-factorizations of bipartite complete graphs We know that the existence of a G−regular 1−factorization of Ks×t necessarily ... existence of a G−regular 1−factorization follows from Proposition Cyclic 1-factorizations of multipartite complete graphs In this section we focus our attention on the cyclic case The cyclic group of...
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effect of processing parameters on pore structure and thickness of anodic
... equilibrium of oxidation and chemical dissolution The dynamic equilibrium of the oxide formation (highly dependent on the acid concentration and availability of oxygen ions) and dissolution (relatively ... molecules once pass into one end (inner) of the pore would only come out from the other end (outer) of the pore without diffusing out from the middle of the pore- tunnel The relationship of membrane thickness ... acid concentration Concentration of the acids also influenced the pore size in a way that higher acid concentration increased the rate of oxidation than dissolution thereby decreasing the pore...
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Báo cáo "Monte carlo simulation by code of MCNP and experimental check for measuring thickness of materials for the specializing system of MYO-101 " ppt
... Journal of Science, Mathematics - Physics 26 (2010) 43-49 includes two parts: i) the theoretical simulation of measuring intensity for thickness of materials by the system of MYO-101 with using code ... versus thickness between simulation by MCNP and experimental measurement for aluminum Fig Comparison of count rate versus thickness between simulation by MCNP and experimental measurement for white ... Comparison of count rate versus thickness between simulation by MCNP and experimental measurement for plastic Fig Comparison of count rate versus thickness between simulation by MCNP and experimental...
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Báo cáo " Local polynomial convexity of union of two graphs with CR isolated singularities" doc
... Quang Dieu, Local polynomial convexity of tangentials union of totally real graphs in C2 , Indag Math., 10 (1999) 349 [3] Nguyen Quang Dieu, Local hulls of union of totally real graphs lying ... Cn , suppose there is polynomial p mapping X1 and X2 into two polynomially convex subsets Y1 and Y2 of the complex plane such that is a boundary point of both Y1 and Y2 and with Y1 ∩ Y2 = {0} If ... denote that [z , f 2; D] is the function algebra which consisting of uniform limit on D of all polynomials in z and f Using polynomial convexity theory, it can be shown that [z , f 2; D] = C(D) for...
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Báo cáo Y học: Stimulated biosynthesis of flavins in Photobacterium phosphoreum IFO 13896 and the presence of complete rib operons in two species of luminous bacteria Sabu Kasai and Takumi Sumimoto pot
... Structural and functional analysis of the riboflavin synthesis genes encoding GTP cyclohydrolase II (ribA), DHBP synthase (ribBA), riboflavin synthase (ribC), and riboflavin deaminase/reductase (ribD) ... Downstream of ribX, four rib genes ) ribD, ribC, ribBA and ribE ) were organized in a complete operon in the same arrangement as the complete rib operons in other species The tail of ribD overlapped ... Homologies of five rib proteins, RibX, RibD, RibC, RibBA and RibE of P phosphoreum or V fischeri with those of seven species Amino acid identity (%) in the sequences of five Rib proteins of P phosphoreum...
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Báo cáo khoa học: "Semantics of Conceptual Graphs" pptx
... Mary Conceptual graphs are a kind of semantic network See Findler ( 9 ) for surveys of a variety of such networks that have been used in AI The diagram above illustrates some features of the conceptual ... illustrated in the diagram, the theory of conceptual graphs includes the following: • For any particular domain of discourse, a specially designated set of conceptual graphs called the canon, • ... implement the theory of conceptual graphs The NLP system processes two kinds of Augmented Informally, a sequent states that if all of the conditions are true, then at least one of the assertions...
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GEOMETRIC PROPERTIES OF CROSS SECTION
... x ’ d~ Zp+Zn = ? + J C y d~ = C r d~ (8.4) 202 Geometrical properties of cross- sections Figure 8.3 Cross- section where J = polar second moment of area = C r d~ (8.5) Equation (8.4) is known as ... RSJs, tees, angle bars etc The geometrical properties of several cross- sections will now be determined Problem 8.1 Determine the second moment of area of the rectangular section about its centroid ... second moment of area about x-x In = the second moment of area about X-X The importance of the parallel axes theorem is that it is useful for calculating second moments of area of sections of RSJs,...
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