排序方式: 共有42条查询结果,搜索用时 140 毫秒
21.
Saharon Shelah Jö rg Brendle Saharon Shelah 《Transactions of the American Mathematical Society》1999,351(7):2643-2674
For a free ultrafilter on we study several cardinal characteristics which describe part of the combinatorial structure of . We provide various consistency results; e.g. we show how to force simultaneously many characters and many -characters. We also investigate two ideals on the Baire space naturally related to and calculate cardinal coefficients of these ideals in terms of cardinal characteristics of the underlying ultrafilter.
22.
Robert Šámal 《Journal of Graph Theory》2017,85(1):56-73
Given two graphs, a mapping between their edge‐sets is cycle‐continuous , if the preimage of every cycle is a cycle. The motivation for this definition is Jaeger's conjecture that for every bridgeless graph there is a cycle‐continuous mapping to the Petersen graph, which, if solved positively, would imply several other important conjectures (e.g., the Cycle double cover conjecture). Answering a question of DeVos, Ne?et?il, and Raspaud, we prove that there exists an infinite set of graphs with no cycle‐continuous mapping between them. Further extending this result, we show that every countable poset can be represented by graphs and the existence of cycle‐continuous mappings between them. 相似文献
23.
Let D be a t ‐ ( v, k , λ) design and let N i (D) , for 1 ≤ i ≤ t , be the higher incidence matrix of D , a ( 0 , 1 )‐matrix of size , where b is the number of blocks of D . A zero‐sum flow of D is a nowhere‐zero real vector in the null space of N 1 ( D ). A zero‐sum k‐flow of D is a zero‐sum flow with values in { 1 , …, ±( k ? 1 )}. In this article, we show that every non‐symmetric design admits an integral zero‐sum flow, and consequently we conjecture that every non‐symmetric design admits a zero‐sum 5‐flow. Similarly, the definition of zero‐sum flow can be extended to N i ( D ), 1 ≤ i ≤ t . Let be the complete design. We conjecture that N t ( D ) admits a zero‐sum 3‐flow and prove this conjecture for t = 2 . © 2011 Wiley Periodicals, Inc. J Combin Designs 19:355‐364, 2011 相似文献
24.
This article determines the set of the circular flow numbers of regular graphs. Let be the set of the circular flow numbers of graphs, and be the set of the circular flow numbers of d‐regular graphs. If d is even, then . For it is known 6 that . We show that . Hence, the interval is the only gap for circular flow numbers of ‐regular graphs between and 5. Furthermore, if Tutte's 5‐flow conjecture is false, then it follows, that gaps for circular flow numbers of graphs in the interval [5, 6] are due for all graphs not just for regular graphs. 相似文献
25.
Tutte's 3‐Flow Conjecture states that every 2‐edge‐connected graph with no 3‐cuts admits a 3‐flow. The 3‐Flow Conjecture is equivalent to the following: let G be a 2‐edge‐connected graph, let S be a set of at most three vertices of G; if every 3‐cut of G separates S then G has a 3‐flow. We show that minimum counterexamples to the latter statement are 3‐connected, cyclically 4‐connected, and cyclically 7‐edge‐connected. 相似文献
26.
This article establishes a relationship between the real (circular) flow number of a graph and its cycle rank. We show that a connected graph with real flow number p/q + 1, where p and q are two relatively prime numbers must have cycle rank at least p + q ? 1. A special case of this result yields that the real flow number of a 2‐connected cubic graph with chromatic index 4 and order at most 8k + 4 is bounded from below by 4 + 1/k. Using this bound we prove that the real flow number of the Isaacs snark I2k + 1 equals 4 + 1/k, completing the upper bound due to Steffen [Steffen, J Graph Theory 36 (2001), 24–34]. © 2008 Wiley Periodicals, Inc. J Graph Theory 59: 11–16, 2008 相似文献
27.
Martin Kochol 《Journal of Graph Theory》2002,40(3):137-146
The tension polynomial FG(k) of a graph G, evaluating the number of nowhere‐zero ?k‐tensions in G, is the nontrivial divisor of the chromatic polynomial χG(k) of G, in that χG(k) = kc(G)FG(k), where c(G) denotes the number of components of G. We introduce the integral tension polynomial IG(k), which evaluates the number of nowhere‐zero integral tensions in G with absolute values smaller than k. We show that 2r(G)FG(k)≥IG(k)≥ (r(G)+1)FG(k), where r(G)=|V(G)|?c(G), and, for every k>1, FG(k+1)≥ FG(k)˙k / (k?1) and IG(k+1)≥IG(k)˙k/(k?1). © 2002 Wiley Periodicals, Inc. J Graph Theory 40: 137–146, 2002 相似文献
28.
29.
Bouchet's conjecture asserts that each signed graph which admits a nowhere‐zero flow has a nowhere‐zero 6‐flow. We verify this conjecture for two basic classes of signed graphs—signed complete and signed complete bipartite graphs by proving that each such flow‐admissible graph admits a nowhere‐zero 4‐flow and we characterise those which have a nowhere‐zero 2‐flow and a nowhere‐zero 3‐flow. 相似文献
30.
For a stationary Gaussian process either almost all sample paths are almost everywhere differentiable or almost all sample paths are almost nowhere differentiable. In this paper it is shown by means of an example involving a random lacunary trigonometric series that “almost everywhere differentiable” and “almost nowhere differentiable” cannot in general be replaced by “everywhere differentiable” and “nowhere differentiable”, respectively. 相似文献