共查询到20条相似文献,搜索用时 31 毫秒
1.
2.
3.
4.
5.
6.
《Journal of Pure and Applied Algebra》2023,227(3):107228
Let be a finite permutation group and recall that the base size of G is the minimal size of a subset of Ω with trivial pointwise stabiliser. There is an extensive literature on base sizes for primitive groups, but there are very few results for primitive groups of product type. In this paper, we initiate a systematic study of bases in this setting. Our first main result determines the base size of every product type primitive group of the form with soluble point stabilisers, where , and is transitive. This extends recent work of Burness on almost simple primitive groups. We also obtain an expression for the number of regular suborbits of any product type group of the form and we classify the groups with a unique regular suborbit under the assumption that P is primitive, which involves extending earlier results due to Seress and Dolfi. We present applications on the Saxl graphs of base-two product type groups and we conclude by establishing several new results on base sizes for general product type primitive groups. 相似文献
7.
8.
9.
10.
11.
12.
13.
《Discrete Mathematics》2022,345(10):113004
Let G be a graph. We say that G is perfectly divisible if for each induced subgraph H of G, can be partitioned into A and B such that is perfect and . We use and to denote a path and a cycle on t vertices, respectively. For two disjoint graphs and , we use to denote the graph with vertex set and edge set , and use to denote the graph with vertex set and edge set . In this paper, we prove that (i) -free graphs are perfectly divisible, (ii) if G is -free with , (iii) if G is -free, and (iv) if G is -free. 相似文献
14.
15.
16.
17.
《Discrete Mathematics》2022,345(8):112903
Graphs considered in this paper are finite, undirected and loopless, but we allow multiple edges. The point partition number is the least integer k for which G admits a coloring with k colors such that each color class induces a -degenerate subgraph of G. So is the chromatic number and is the point arboricity. The point partition number with was introduced by Lick and White. A graph G is called -critical if every proper subgraph H of G satisfies . In this paper we prove that if G is a -critical graph whose order satisfies , then G can be obtained from two non-empty disjoint subgraphs and by adding t edges between any pair of vertices with and . Based on this result we establish the minimum number of edges possible in a -critical graph G of order n and with , provided that and t is even. For the corresponding two results were obtained in 1963 by Tibor Gallai. 相似文献
18.
19.
20.
In this paper we provide the sharp conditions of the uniqueness for inverse nodal Sturm–Liouville problems defined on interval with separated boundary conditions. We prove that the potential and boundary parameters can be uniquely determined by a dense nodal subset contained on with through two cases of and , where in the latter case the nodal subset also need to be paired. Note that, the dense nodal subset was required to be twin for both cases in the previous works. 相似文献