Useful Lemmas for the proof of Theorem 4
3 Proof of Theorem 6
... Theorem 10. Let S be a connected graph with S = P 3 and let G be a 2-connected claw-f 1 -heavy graph which is not a cycle. Then G being S-f 1 -heavy implies G is pancyclic if S = P 4 , Z 1 or Z 2 . The ...
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4. Proof of the theorem
... 22 (1, 1) rr r ! = ∞ whenever p 6= r. The reasoning in the previous lemmas will not help us now, since in Lemma 4.2 we needed c < ∞. As we shall see in Proposition 5.1, the proof for c = ∞ must use lower ...
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A Proof of Theorem 1.2
... Throughout, we let to denote an infinitesimal quantity. Notice that if any misprediction is found or job 1 is finished in stage 1, the algorithm is equivalent of round robin and, therefore, achieves 4/3 ...
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A. Proof of Theorem 1
... We test out the effect of different matrix properties. For vanilla, we sample the matrix entries from a normal distribution. Next, we apply a ReLU operation after each multiplication. For ReLU learned, we used the ...
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M PROOF OF THE DIVERGENCE THEOREM AND STOKES THEOREM
... Divergence Theorem, we use the same approach as we used for Green’s Theorem; first prove the theorem for rectangular regions, then use the change of variables formula to prove it for regions ...
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2 Proof of Theorem 1.15
... Theorem 1.8 ([1, 2, 3 ]) For n ∈ {3, 4, 5, 6, 7} and all k ≥ 1, GR k (C 2n+1 ) = n · 2 k + 1. In this paper, we study Gallai-Ramsey numbers of even cycles and paths. Note that GR k (H) = |H| for any graph H ...
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2 Proof of Theorem 1
... combinatorial proof of the rank-unimodality of the poset of order ideals of a product of chains of lengths 2, n, and m, and find a symmetric chain decomposition in the case where n = ...
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3 Proof of Theorem 1.8
... Bollobás’ proof [3, pages 48–49] of the Erdős–Ko–Rado (EKR) Theorem [9], and we make some observations regarding the values p n,k and the structure of t-intersecting subsets of P n,k ...
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2 Proof of the main theorem
... This question differs from classic coin-weighing problems in that we do not need to discover the weights, but only to determine whether or not a given labeling of weights is the correct one. To establish the weights one ...
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3 Proof of Theorem 2.7
... (4) Extension theorems are often used for optimal linear codes problem, especially to prove the nonexistence of linear codes with certain parameters.. Moreover, the extended matrix of G [r] ...
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3 Proof of Theorem 3
... x 4 z 4 z 5 z 1 ...the proof of the lemma. 3 Proof of Theorem 3 Let n, s, and t be integers with n = 3s + 5t, s ≥ 1, t ≥ ...Lemma 4, G contains t independent ...the ...
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3 Proof of the main theorem
... Claim 3 G is the union of stars and at most one double star. Moreover, if H has no double stars, then G also has no double stars. We may assume that k ≥ 4 since otherwise H ∈ F ∞ ∪ {P 4 }. Assume that G has ...
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3 Proof of Theorem 1.2
... A vector ~y ∈ S is called an optimal vector of λ(G) if λ(G, ~y) = λ(G). The following fact is easily implied by the definition of the Lagrange function. Fact 2.1 Let G 1 , G 2 be r-uniform graphs and G 1 ⊂ G 2 . Then λ(G ...
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3. Proof of Theorem 2.11
... 3. Proof of Theorem 2.11 We provide a proof for the case of f h , the interested reader is invited to carry out the dual part of Theorem ...
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An Informational Proof of H Theorem
... for determining anti-random aspects that concern with the biological functions emerging during evolution. In conclusion, the discrete and computational per- spectives are ingredients that are missing in classical ...
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A Simple Proof of a Theorem by Harris
... 1 Introduction This note presents a simple proof of a theorem by Harris [4] on the existence of subgame perfect equilibria in games of perfect information. More generally, it illustrates a method for ...
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A duality proof of Tchakaloff's theorem
... implies that it has a unique representing measure, whence µ = ν. ✷ Note added in proof. We have recently learned from Professor Christian Berg that the weak- ∗ convergence techniques used in the proof of ...
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A Proof of the Jordan Curve Theorem
... The proof of the Jordan Curve Theorem (JCT) in this paper is focused on a graphic illustra- tion and analysis ways so as to make the topological proof more understandable, and is based on the ...
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2 Proof of Theorem 1
... 1 Introduction Embeddings of finite metric spaces into Euclidean spaces or other normed spaces that approximately preserve the metric received considerable attention in recent years. Numerous significant results have been ...
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3 Proof of the Theorem 3
... In this paper we obtain existence results for the positive solution of a singular elliptic boundary value problem.. Our study is motivated by the works of Shu [17], Arcoya, Carmona, Leon[r] ...
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