Bipartite subgraphs of graphs with maximum degree three

被引：7
|
作者：
Bylka, SA [1 ]
Idzik, A [1 ]
Komar, J [1 ]
机构：
[1] Polish Acad Sci, Inst Comp Sci, PL-02137 Warsaw, Poland
来源：
GRAPHS AND COMBINATORICS | 1999年 / 15卷 / 02期
关键词：
bipartite graph; n-colourable graph; extremal graph;
D O I：
10.1007/s003730050047
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We prove that for a connected graph G with maximum degree 3 there exists a bipartite subgraph of G containing almost 3/4 of the edges of G. Furthermore, we completely characterize the set of all extremal graphs, i.e. all connected graphs G = (V, E) with maximum degree 3 for which no bipartite subgraph has more than 3 \E\ - 1/4 of the edges; \E\ denotes the cardinality of E. For 2-edge-connected graphs there are two kinds of extremal graphs which realize the lower bound 3/4 \E\.
引用
收藏
页码：129 / 136
页数：8
相关论文
共 50 条
  • [21] Bipartite subgraphs of integer weighted graphs
    Alon, N
    Halperin, E
    DISCRETE MATHEMATICS, 1998, 181 (1-3) : 19 - 29
  • [22] ON RAMSEY GRAPHS WITHOUT BIPARTITE SUBGRAPHS
    NESETRIL, J
    RODL, V
    DISCRETE MATHEMATICS, 1992, 101 (1-3) : 223 - 229
  • [23] On covering graphs by complete bipartite subgraphs
    Jukna, S.
    Kulikov, A. S.
    DISCRETE MATHEMATICS, 2009, 309 (10) : 3399 - 3403
  • [24] Maximum values of degree-based entropies of bipartite graphs
    Dong, Yanni
    Qiao, Shengning
    Chen, Bing
    Wan, Pengfei
    Zhang, Shenggui
    APPLIED MATHEMATICS AND COMPUTATION, 2021, 401
  • [25] Decomposition of bipartite graphs into special subgraphs
    Chen, Guantao
    Schelp, Richard H.
    DISCRETE APPLIED MATHEMATICS, 2007, 155 (03) : 400 - 404
  • [26] Large homogeneous subgraphs in bipartite graphs with forbidden induced subgraphs
    Axenovich, Maria
    Tompkins, Casey
    Weber, Lea
    JOURNAL OF GRAPH THEORY, 2021, 97 (01) : 34 - 46
  • [27] Subgraphs of maximum matching graphs
    Yan, L
    INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 2004, 35 (09): : 1063 - 1067
  • [28] OPTIMAL ORIENTATIONS OF SUBGRAPHS OF COMPLETE BIPARTITE GRAPHS
    Lakshmi, R.
    Rajasekaran, G.
    Sampathkumar, R.
    TRANSACTIONS ON COMBINATORICS, 2015, 4 (01) : 19 - 29
  • [29] BIPARTITE SUBGRAPHS OF H-FREE GRAPHS
    Zeng, Qinghou
    Hou, Jianfeng
    BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2017, 96 (01) : 1 - 13
  • [30] A METHOD FOR FINDING EXTREMAL SUBGRAPHS IN BIPARTITE GRAPHS
    GORSHKOV, AF
    SOVIET JOURNAL OF COMPUTER AND SYSTEMS SCIENCES, 1987, 25 (01): : 85 - 91
12345