Subgraph-avoiding minimum decycling sets and k-conversion sets in graphs

被引：0
|
作者：
Francis, M. D. [1 ]
Mynhardt, C. M. [2 ]
Wodlinger, J. L. [3 ]
机构：
[1] Penn State Univ, Dept Math, University Pk, PA 16802 USA
[2] Univ Victoria, Dept Math & Stat, POB 3045, Victoria, BC V8W 3P4, Canada
[3] Vancouver Isl Univ, Dept Math, 900 Fifth St, Nanaimo, BC V9R 5S5, Canada
来源：
AUSTRALASIAN JOURNAL OF COMBINATORICS | 2019年 / 74卷
基金：
加拿大自然科学与工程研究理事会;
关键词：
FEEDBACK VERTEX SETS; INDUCED FORESTS; ARC;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A decycling set of a graph G is a set S of vertices such that G[V - S] is acyclic. In this paper we prove that every non- complete graph G of maximum degree r >= 3 has a minimum decycling set S such that G[S] does not contain an (r-2)- regular graph as a subgraph. This generalizes a result in [P.A. Catlin and H.-J. Lai, Discrete Math. 141(1) (1995), 37- 46]. We give several consequences of our main result, including new proofs of known results.
引用
收藏
页码：288 / 304
页数：17
相关论文
共 50 条
  • [21] Block graphs with unique minimum dominating sets
    Fischermann, M
    [J]. DISCRETE MATHEMATICS, 2001, 240 (1-3) : 247 - 251
  • [22] ON DEGREE SETS AND THE MINIMUM ORDERS IN BIPARTITE GRAPHS
    Manoussakis, Y.
    Patil, H. P.
    [J]. DISCUSSIONES MATHEMATICAE GRAPH THEORY, 2014, 34 (02) : 383 - 390
  • [23] Graphs with Unique Minimum Specified Domination Sets
    Goddard, Wayne
    Henning, Michael A. A.
    [J]. GRAPHS AND COMBINATORICS, 2023, 39 (05)
  • [24] On Independent Sets in Graphs with Given Minimum Degree
    Law, Hiu-Fai
    Mcdiarmid, Colin
    [J]. COMBINATORICS PROBABILITY & COMPUTING, 2013, 22 (06): : 874 - 884
  • [25] Reconfiguring Minimum Independent Dominating Sets in Graphs
    Brewster, R. C.
    Mynhardt, C. M.
    Teshima, L. E.
    [J]. COMMUNICATIONS IN COMBINATORICS AND OPTIMIZATION, 2024, 9 (03) : 389 - 411
  • [26] Cactus graphs with unique minimum dominating sets
    Fischermann, M
    Volkmann, L
    [J]. UTILITAS MATHEMATICA, 2003, 63 : 229 - 238
  • [27] Reconfiguration of Minimum Independent Dominating Sets in Graphs
    Brewster, R.C.
    Mynhardt, C.M.
    Teshima, L.E.
    [J]. arXiv, 2023,
  • [28] SETS OF INDEPENDENT VERTICES IN MINIMUM CHROMATIC GRAPHS
    BROWN, WG
    MOON, JW
    [J]. CANADIAN JOURNAL OF MATHEMATICS, 1969, 21 (02): : 274 - &
  • [29] Minimum connected dominating sets and maximal independent sets in unit disk graphs
    Wu, WL
    Du, HW
    Jia, XH
    Li, YS
    Huang, SCH
    [J]. THEORETICAL COMPUTER SCIENCE, 2006, 352 (1-3) : 1 - 7
  • [30] Graphs such that All Minimum Dominating Sets Intersect All Maximally Independent Sets
    Johnson, P. D., Jr.
    Prier, D. R.
    [J]. UTILITAS MATHEMATICA, 2012, 89 : 211 - 224
12345