共查询到20条相似文献,搜索用时 31 毫秒
1.
Haiyang Zhu Lianying Miao Sheng Chen Xinzhong Lü Wenyao Song 《Discrete Mathematics》2018,341(8):2211-2219
Let be the set of all positive integers. A list assignment of a graph is a function that assigns each vertex a list for all . We say that is --choosable if there exists a function such that for all , if and are adjacent, and if and are at distance 2. The list--labeling number of is the minimum such that for every list assignment , is --choosable. We prove that if is a planar graph with girth
and its maximum degree is large enough, then . There are graphs with large enough and having . 相似文献
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Denis S. Krotov 《Discrete Mathematics》2017,340(12):2723-2731
A subspace bitrade of type is a pair of two disjoint nonempty collections of -dimensional subspaces of a -dimensional space over the finite field of order such that every -dimensional subspace of is covered by the same number of subspaces from and . In a previous paper, the minimum cardinality of a subspace bitrade was established. We generalize that result by showing that for admissible , , and , the minimum cardinality of a subspace bitrade does not depend on . An example of a minimum bitrade is represented using generator matrices in the reduced echelon form. For , the uniqueness of a minimum bitrade is proved. 相似文献
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Boris Brimkov Jennifer Edmond Robert Lazar Bernard Lidický Kacy Messerschmidt Shanise Walker 《Discrete Mathematics》2017,340(10):2538-2549
An injective coloring of a graph is an assignment of colors to the vertices of so that any two vertices with a common neighbor have distinct colors. A graph is injectively -choosable if for any list assignment , where for all , has an injective -coloring. Injective colorings have applications in the theory of error-correcting codes and are closely related to other notions of colorability. In this paper, we show that subcubic planar graphs with girth at least 6 are injectively 5-choosable. This strengthens the result of Lu?ar, ?krekovski, and Tancer that subcubic planar graphs with girth at least 7 are injectively 5-colorable. Our result also improves several other results in particular cases. 相似文献
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The solution to a set theory exercise, “Partition the set of positive integers into subsets such that the sum of the elements in each subset is whenever is an integer”, gives a construction of non-simple 1-SB designs. This raises a natural question of the existence of simple 1-SB designs. We show that the necessary conditions for the existence of simple 1-SB designs for block sizes 2, 3, 4, 5 and 6 are sufficient. Moreover, the technique exhibited in the proof can be applied to block sizes greater than . We also show that simple , and designs do not exist for any positive integers and .A natural question, “Can we obtain a construction for simple 1-SB designs similar to Billington’s classical construction of simple 1-designs for any block size ?”, remains open. 相似文献
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We consider the system of nonlinear wave equations with initial and Dirichlet boundary conditions. Under some suitable assumptions on the functions, , , , parameters and the initial data, the result on blow-up of solutions and upper bound of blow-up time are given. 相似文献
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Carl Johan Casselgren Hrant H. Khachatrian Petros A. Petrosyan 《Discrete Mathematics》2018,341(3):627-637
An interval-coloring of a multigraph is a proper edge coloring with colors such that the colors of the edges incident with every vertex of are colored by consecutive colors. A cyclic interval-coloring of a multigraph is a proper edge coloring with colors such that the colors of the edges incident with every vertex of are colored by consecutive colors, under the condition that color is considered as consecutive to color . Denote by () and () the minimum and maximum number of colors in a (cyclic) interval coloring of a multigraph , respectively. We present some new sharp bounds on and for multigraphs satisfying various conditions. In particular, we show that if is a -connected multigraph with an interval coloring, then . We also give several results towards the general conjecture that for any triangle-free graph with a cyclic interval coloring; we establish that approximate versions of this conjecture hold for several families of graphs, and we prove that the conjecture is true for graphs with maximum degree at most . 相似文献
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A proper total weighting of a graph is a mapping which assigns to each vertex and each edge of a real number as its weight so that for any edge of , . A -list assignment of is a mapping which assigns to each vertex a set of permissible weights and to each edge a set of permissible weights. An -total weighting is a total weighting with for each . A graph is called -choosable if for every -list assignment of , there exists a proper -total weighting. It was proved in Tang and Zhu (2017) that if , a graph without isolated edges and with is -choosable. In this paper, we strengthen this result by showing that for any prime , a graph without isolated edges and with is -choosable. 相似文献
10.
Jeffrey A. Mudrock 《Discrete Mathematics》2018,341(11):3148-3151
DP-coloring (also called correspondence coloring) is a generalization of list coloring recently introduced by Dvo?ák and Postle. Several known bounds for the list chromatic number of a graph , , also hold for the DP-chromatic number of , . On the other hand, there are several properties of the DP-chromatic number that show that it differs with the list chromatic number. In this note we show one such property. It is well known that if and only if . We show that if , and we show that if . 相似文献
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Christoph Brause Arnfried Kemnitz Massimiliano Marangio Anja Pruchnewski Margit Voigt 《Discrete Mathematics》2017,340(11):2633-2640
Let be a simple graph and for every vertex let be a set (list) of available colors. is called -colorable if there is a proper coloring of the vertices with for all . A function is called a choice function of and is said to be -list colorable if is -colorable for every list assignment choice function is defined by and the sum choice number
denotes the minimum size of a choice function of .Sum list colorings were introduced by Isaak in 2002 and got a lot of attention since then.For a generalized
-graph is a simple graph consisting of two vertices and connected by internally vertex disjoint paths of lengths
.In 2014, Carraher et al. determined the sum-paintability of all generalized -graphs which is an online-version of the sum choice number and consequently an upper bound for it.In this paper we obtain sharp upper bounds for the sum choice number of all generalized -graphs with and characterize all generalized -graphs which attain the trivial upper bound . 相似文献
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《Discrete Mathematics》2007,307(7-8):916-922
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《Nonlinear Analysis: Hybrid Systems》2007,1(1):124-134
Convolution complementarity problems have the form: given a kernel function and a function , find a function such that , for (almost) all , and where . A fractional index problem of this kind has for small, with . Such problems are shown to have unique solutions under mild conditions. 相似文献
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Zhi-Hong Chen 《Discrete Mathematics》2017,340(12):3104-3115
For a graph , let and let . We show that for a given number and given integers , and , if is a -connected claw-free graph of order with and its Ryjác?ek’s closure , and if where , then either is Hamiltonian or , the preimage of , can be contracted to a -edge-connected -free graph of order at most and without spanning closed trails. As applications, we prove the following for such graphs of order with sufficiently large:(i) If , , and for a given () , then either is Hamiltonian or where is a graph obtained from by replacing each of the degree 2 vertices by a (). When and , this proves a conjecture in Frydrych (2001).(ii) If , , and for a given () , then is Hamiltonian. These bounds on in (i) and (ii) are sharp. It unifies and improves several prior results on conditions involved and for the hamiltonicity of claw-free graphs. Since the number of graphs of orders at most are fixed for given , improvements to (i) or (ii) by increasing the value of are possible with the help of a computer. 相似文献
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György Gát 《Journal of Approximation Theory》2012,164(1):145-161
Let be the lower integer part of the binary logarithm of the positive integer and . In this paper we generalize the notion of the two dimensional Marcinkiewicz means of Fourier series of two-variable integrable functions as and give a kind of necessary and sufficient condition for functions in order to have the almost everywhere relation for all with respect to the Walsh–Paley system. The original version of the Marcinkiewicz means are defined by and discussed by a lot of authors. See for instance [13], [8], [6], [3], [11]. 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