Bisplit graphs satisfy the Chen-Chvatal conjecture

被引：0

作者：

Beaudou, Laurent ^{[1
]}

Kahn, Giacomo ^{[2
]}

Rosenfeld, Matthieu ^{[3
]}

机构：

[1] Higher Sch Econ, Moscow, Russia

[2] Univ Orleans, Orleans, France

[3] Univ Liege, Liege, Belgium

来源：

DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE | 2019年 / 21卷 / 01期

关键词：

bisplit graphs; Chen-Chvatal conjecture; distances;

D O I：

暂无

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

In this paper, we give a lengthy proof of a small result! A graph is bisplit if its vertex set can be partitioned into three stable sets with two of them inducing a complete bipartite graph. We prove that these graphs satisfy the Chen-Chvatal conjecture: their metric space (in the usual sense) has a universal line (in an unusual sense) or at least as many lines as the number of vertices.

引用

页数：12

共 50 条

[1] A New Class of Graphs That Satisfies the Chen-Chvatal Conjecture
Aboulker, P.
Matamala, M.
Rochet, P.
Zamora, J.
[J]. JOURNAL OF GRAPH THEORY, 2018, 87 (01) : 77 - 88
[2] The Chen-Chvatal conjecture for metric spaces induced by distance-hereditary graphs
Aboulker, Pierre
Kapadia, Rohan
[J]. EUROPEAN JOURNAL OF COMBINATORICS, 2015, 43 : 1 - 7
[3] Solution of the Chen-Chvatal conjecture for specific classes of metric spaces
Rodriguez-Velazquez, Juan Alberto
[J]. AIMS MATHEMATICS, 2021, 6 (07): : 7766 - 7781
[4] Chen and Chvatal's conjecture in tournaments
Araujo-Pardo, Gabriela
Matamala, Martin
[J]. EUROPEAN JOURNAL OF COMBINATORICS, 2021, 97
[5] UNICYCLIC GRAPHS SATISFY HARARYS CONJECTURE
ARJOMANDI, E
CORNEIL, DG
[J]. CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 1974, 17 (04): : 593 - 595
[6] Bisplit graphs
Brandstädt, A
Hammer, PL
Le, VB
Lozin, VV
[J]. DISCRETE MATHEMATICS, 2005, 299 (1-3) : 11 - 32
[7] Proof of Chvatal's conjecture on maximal stable sets and maximal cliques in graphs
Deng, XT
Li, GJ
Zang, WN
[J]. JOURNAL OF COMBINATORIAL THEORY SERIES B, 2004, 91 (02) : 301 - 325
[8] A Larger Family of Planar Graphs that Satisfy the Total Coloring Conjecture
Leidner, Maxfield
[J]. GRAPHS AND COMBINATORICS, 2014, 30 (02) : 377 - 388
[9] A Larger Family of Planar Graphs that Satisfy the Total Coloring Conjecture
Maxfield Leidner
[J]. Graphs and Combinatorics, 2014, 30 : 377 - 388
[10] A note on the recognition of bisplit graphs
Abueida, Atif
Sritharan, R.
[J]. DISCRETE MATHEMATICS, 2006, 306 (17) : 2108 - 2110

← 1 2 3 4 5 →