Báo cáo toán học: "On the number of perfect matchings and Hamilton cycles in -regular non-bipartite graphs" ppsx
Báo cáo toán học: "On the number of perfect matchings and Hamilton cycles in -regular non-bipartite graphs" ppsx
... n)k−1φ(k). In either case, the inequality in part 1 of the lemma holds.On the number of perfect matchings and Hamilton cycles in -regular non-bipartite graphsAlan Frieze∗Department of Mathematical ... of combinatorics 7 (2000), #R57 43 Hamilton Cycles A Hamilton cycle is the union of two perfect matchings and so h(G) ≤12m(G)2 and the upper bound in part (b) of Theorem 1 follows from the ... segment containing x, the segment containing x, and the remaining segment.Going round the cycle Ci, starting at x and ending at x, the vertices x, x,y,y,z,zmay appear in one of eight...
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Báo cáo toán học: "On the number of possible row and column sums of 0,1-matrices" pps
... ,an)=a(x)inNn+1.Wenotethat|a| = m,andwritemafor the multinomial coefficientm!a0!···an!With this notation, we have the following lemma.Lemma 6 Let a in Nn+1satisfy |a| = m. Then the number of x in Nmsuch ... combinatorics 13 (2006), #N8 53 Start of the proofLet N = {0, 1, }. Define the weight of a matrix N to be the sum of its entries, and write |N| for the weight of N. With this definition, we have ... on the right is a polynomial of total degree at most n. This is true for the first termN((λ1, ,λn−1)) by the inductive hypothesis.Each of the subsequent terms is itself a sum. By the inductive...
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Báo cáo toán học: "On the number of subsequences with a given sum in a finite abelian grou" pptx
... g of G, the lower bound of Ng(S) remains undetermined. In this paper, we determine the best possible lower bound of Ng(S) for an arbitraryg of G. We also characterize the structures of the ... Tianjin 300071, P.R. China5Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160, P.R. China6Department of Mathematics, Harbin University of Science and Technology, Harbin ... sequence of elements in G. Forany element g of G, let Ng(S) denote the number of subsequences of S with sumg. The purpose of this paper is to investigate the lower bound for Ng(S). In particular,...
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Báo cáo toán học: " ON THE NUMBER OF DESCENDANTS AND ASCENDANTS IN RANDOM SEARCH TREES" ppsx
... +1)649n6.7. The number of ascendants of a given node in a LBSTAs in the case of the number of ascendants in a random BST, computing the probability that the jthnode in a random LBST has ... JOURNAL OF COMBINATORICS 5 (1998), #R20 83. The number of descendants in random BSTs The number of the descendants Dn,j of the jthnode of a BST of size n is recursively computedas the number of ... uzwhere the Ci(z,u)’s are polynomials in z and u. They have been listed in the appendix. Usingtechniques similar to the ones in the proof of Theorem 6.2, we extract the coefficients and obtainthe...
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Báo cáo toán học: "On the number of permutations admitting an m-th root" pptx
... 800 1000Figure 1: The function m → κm4.3. Statement and pro of of the main theorem The situation is the following: we look for the asymptotics of the coefficientspn(m) of the formal series ... is not the case. We approximate the cn(m) by the coefficients dn(m) of the expan-sion in power series of the principal part Dm of Cm in a neighbourhood of its dominantsingularity 1. The sequencesdn−k(m)/dn(m)nare ... is the exponential generating function (EGF, formal series) of the m-thpowersinthegroupsn. This means that the number of m-thpowersinnispn(m)×n!foreachn.Inthesameway,Cmis the EGF of the...
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Báo cáo toán học: " ON THE NUMBER OF FULLY PACKED LOOP CONFIGURATIONS WITH A FIXED" pot
... points of the planar integer lattice Z2,such that for all i<jthe point Aiis (weakly) south-east of the point Aj, and the pointEiis (weakly) south-east of the point Ej. Then the number ... every other horizontal edge in the region BCLK as indicated in the figure,(4) the zig-zag lines in the corner regions above the line EA, respectively below the lines DM and MC, as indicated in the ... X, on the one hand, and to all the external links corresponding to the mnested arches which are on the right of the centre M plus the “last” external link of the matching X, on the other hand....
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Báo cáo toán học: "On the number of orthogonal systems in vector spaces over finite fields" ppsx
... o(1))|E|kk!q−(k2),completing the proof of Theorem 1.2.Acknowledgments The research is performed during the author’s visit at the Erwin Schr¨odinger InternationalInstitute for Mathematical Physics. The author ... From (2.6) and (2.8), the number of copies of Kk in E is(1 + o(1))|E|kk!q−(k2)..This implies that the number of the number of k-tuples of k mutually orthogonalvectors in E is also(1 ... multiple of the other by an element of the field. Let GP(q, d) denote the graph whose vertices are the points of P G(q, d) and two(not necessarily distinct) vertices x and y are adjacent if and...
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Báo cáo toán học: "On the number of genus one labeled circle trees" doc
... E1is the intersection of {E1, E2,. . .,Ek+1} and the points of one of the e-graphs, and point Ek+1is the intersection of {E1, E2, . . . , Ek+1} and the points of the other of the e-graphs.Theorem ... K1 and K2are identical. This can happen onlyifn−22is even (since if K1 and K2are identical, then the number of edges in K1 and K2is the same, thus the sum of the number of edges in ... the points on the other arc of the e-graph in clockwisedirection, so {e1, e2} = {X1Y1, XmYm}. (Note that the number of points on the two arcs of the e-graph is the same since they...
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Báo cáo toán học: "On the Number of Planar Orientations with Prescribed Degrees" pptx
... is sandwiched betweenthat of G2k−2,2−2 and that of G2k,2. Therefore the asymptotic behavior is the same and in [24], the limit of the number of perfect matchings of G2k,2, denoted as Φ(2k, ... but using that we know the number of edges exactly. Since in the independent set of the remaining face vertices all of themhave degree 4 and required out-degree 3, they contribute a factor of 1/2 ... the number of 2-factors of G. Among the 2-factors of G(k) let S denote the set of those, which induce a 2-factor of G, and Sc the other 2-factors. We have|S| = cG· bk·n(i−3)isince the...
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Báo cáo toán học: "On the Number of Matchings in Regular Graphs" pptx
... its subset of bipartite graphs, we characterize the optimal graphswho maximize and minimize the number of m -matchings. We find the expected value of the number of m -matchings of r-regular bipar-tite ... of m. In the expression for φ(G, 4) the number of 4 -cycles appeared as the first structure in the graph, apart from n and r, which affects the number of matchings. The maximumpossible value of a4(G) ... all these choices to get the numerator of the right-hand side of (4.10). Dividethis number of choices by the number of permutations of {1, . . . , rn} to deduce the lemma.✷Using the methods in...
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