共查询到20条相似文献,搜索用时 62 毫秒
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A chord diagram is a set of chords of a circle such that no pair of chords has a common endvertex. A chord diagram is called nonintersecting if contains no crossing. For a chord diagram having a crossing , the expansion of with respect to is to replace with or . For a chord diagram , let be the chord expansion number of , which is defined as the cardinality of the multiset of all nonintersecting chord diagrams generated from with a finite sequence of expansions.In this paper, it is shown that the chord expansion number equals the value of the Tutte polynomial at the point for the interlace graph corresponding to . The chord expansion number of a complete multipartite chord diagram is also studied. An extended abstract of the paper was published (Nakamigawa and Sakuma, 2017) [13]. 相似文献
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Xiuyun Wang 《Discrete Mathematics》2017,340(12):3016-3019
The double generalized Petersen graph , and , , has vertex-set , edge-set . These graphs were first defined by Zhou and Feng as examples of vertex-transitive non-Cayley graphs. Then, Kutnar and Petecki considered the structural properties, Hamiltonicity properties, vertex-coloring and edge-coloring of , and conjectured that all are Hamiltonian. In this paper, we prove this conjecture. 相似文献
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Serhii Dyshko 《Discrete Mathematics》2018,341(11):2995-3002
For a finite vector space over , there are described all the pairs of multisets and of subspaces in such that for all the equality holds. 相似文献
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Kiyoshi Ando 《Discrete Mathematics》2018,341(11):3003-3009
An edge of a -connected graph is said to be -contractible if the contraction of the edge results in a -connected graph. If every -connected graph with no -contractible edge has either or as a subgraph, then an unordered pair of graphs is said to be a forbidden pair for -contractible edges. We prove that is a forbidden pair for 6-contractible edges, which is an extension of a previous result due to Ando and Kawarabayashi. 相似文献
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DP-coloring of a simple graph is a generalization of list coloring, and also a generalization of signed coloring of signed graphs. It is known that for each , every planar graph without is 4-choosable. Furthermore, Jin et al. (2016) showed that for each , every signed planar graph without is signed 4-choosable. In this paper, we show that for each , every planar graph without is 4-DP-colorable, which is an extension of the above results. 相似文献
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Elena Rubei 《Discrete Mathematics》2012,312(19):2872-2880
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The conservative number of a graph is the minimum positive integer , such that admits an orientation and a labeling of its edges by distinct integers in , such that at each vertex of degree at least three, the sum of the labels on the in-coming edges is equal to the sum of the labels on the out-going edges. A graph is conservative if . It is worth noting that determining whether certain biregular graphs are conservative is equivalent to find integer Heffter arrays.In this work we show that the conservative number of a galaxy (a disjoint union of stars) of size is for , , and otherwise. Consequently, given positive integers , , …, with for , we construct a cyclic -cycle system of infinitely many circulant graphs, generalizing a result of Bryant, Gavlas and Ling (2003). In particular, it allows us to construct a cyclic -cycle system of the complete graph , where . Also, we prove necessary and sufficient conditions for the existence of a cyclic -cycle system of , where is a 1-factor. Furthermore, we give a sufficient condition for a subset of to be sequenceable. 相似文献
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Neil J.Y. Fan Peter L. Guo Grace L.D. Zhang 《Journal of Pure and Applied Algebra》2017,221(1):237-250
Parabolic R-polynomials were introduced by Deodhar as parabolic analogues of ordinary R-polynomials defined by Kazhdan and Lusztig. In this paper, we are concerned with the computation of parabolic R-polynomials for the symmetric group. Let be the symmetric group on , and let be the generating set of , where for , is the adjacent transposition. For a subset , let be the parabolic subgroup generated by J, and let be the set of minimal coset representatives for . For in the Bruhat order and , let denote the parabolic R-polynomial indexed by u and v. Brenti found a formula for when , and obtained an expression for when . In this paper, we provide a formula for , where and i appears after in v. It should be noted that the condition that i appears after in v is equivalent to that v is a permutation in . We also pose a conjecture for , where with and v is a permutation in . 相似文献
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José E. Figueroa-López Yankeng Luo 《Stochastic Processes and their Applications》2018,128(12):4207-4245
In this article, we consider a Markov process , which solves a stochastic differential equation driven by a Brownian motion and an independent pure jump component exhibiting both state-dependent jump intensity and infinite jump activity. A second order expansion is derived for the tail probability in small time , where is the initial value of the process and . As an application of this expansion and a suitable change of the underlying probability measure, a second order expansion, near expiration, for out-of-the-money European call option prices is obtained when the underlying stock price is modeled as the exponential of the jump–diffusion process under the risk-neutral probability measure. 相似文献
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TextFor any given two positive integers and , and any set A of nonnegative integers, let denote the number of solutions of the equation with . In this paper, we determine all pairs of positive integers for which there exists a set such that for all . We also pose several problems for further research.VideoFor a video summary of this paper, please click here or visit http://www.youtube.com/watch?v=EnezEsJl0OY. 相似文献