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
  • [31] DECOMPOSITION OF PRODUCT GRAPHS INTO COMPLETE BIPARTITE SUBGRAPHS
    REZNICK, B
    TIWARI, P
    WEST, DB
    DISCRETE MATHEMATICS, 1985, 57 (1-2) : 189 - 193
  • [32] DENSE INDUCED SUBGRAPHS OF DENSE BIPARTITE GRAPHS
    McCarty, Rose
    SIAM JOURNAL ON DISCRETE MATHEMATICS, 2021, 35 (02) : 661 - 667
  • [33] Covering graphs with few complete bipartite subgraphs
    Fleischner, Herbert
    Mujuni, Egbert
    Paulusma, Daniel
    Szieder, Stefan
    THEORETICAL COMPUTER SCIENCE, 2009, 410 (21-23) : 2045 - 2053
  • [34] Covering graphs with few complete bipartite subgraphs
    Fleischner, Herbert
    Mujuni, Egbert
    Paulusma, Daniel
    Szeider, Stefan
    FSTTCS 2007: FOUNDATIONS OF SOFTWARE TECHNOLOGY AND THEORETICAL COMPUTER SCIENCE, PROCEEDINGS, 2007, 4855 : 340 - +
  • [35] EIGENSHARP GRAPHS - DECOMPOSITION INTO COMPLETE BIPARTITE SUBGRAPHS
    KRATZKE, T
    REZNICK, B
    WEST, D
    TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1988, 308 (02) : 637 - 653
  • [36] DECOMPOSITIONS OF COMPLETE GRAPHS INTO ISOMORPHIC BIPARTITE SUBGRAPHS
    BALAKRISHNAN, R
    KUMAR, RS
    GRAPHS AND COMBINATORICS, 1994, 10 (01) : 19 - 25
  • [37] UNIVERSAL GRAPHS WITHOUT LARGE BIPARTITE SUBGRAPHS
    KOMJATH, P
    PACH, J
    MATHEMATIKA, 1984, 31 (62) : 282 - 290
  • [38] On Maximal Chain Subgraphs and Covers of Bipartite Graphs
    Calamoneri, Tiziana
    Gastaldello, Mattia
    Mary, Arnaud
    Sagot, Marie-France
    Sinaimeri, Blerina
    Combinatorial Algorithms, 2016, 9843 : 137 - 150
  • [39] BIPARTITE SUBGRAPHS OF TRIANGLE-FREE GRAPHS
    POLJAK, S
    TUZA, Z
    SIAM JOURNAL ON DISCRETE MATHEMATICS, 1994, 7 (02) : 307 - 313
  • [40] Discovering Hierarchy of Bipartite Graphs with Cohesive Subgraphs
    Wang, Kai
    Zhang, Wenjie
    Lin, Xuemin
    Zhang, Ying
    Li, Shunyang
    2022 IEEE 38TH INTERNATIONAL CONFERENCE ON DATA ENGINEERING (ICDE 2022), 2022, : 2291 - 2305
12345