Degree sums for edges and cycle lengths in graphs

被引：0

作者：

Brandt, S ^{[1
]}

Veldman, HJ ^{[1
]}

机构：

[1] UNIV TWENTE,FAC APPL MATH,NL-7500 AE ENSCHEDE,NETHERLANDS

来源：

JOURNAL OF GRAPH THEORY | 1997年 / 25卷 / 04期

关键词：

degree sum; circumference; cycle hamiltonian graph; pancyclic graph; tough graph; closure;

D O I：

10.1002/(SICI)1097-0118(199708)25:4<253::AID-JGT2>3.0.CO;2-J

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let G be a graph of order n, satisfying d(u) + d(v) greater than or equal to n,for every edge uv of G. We show that the circumference - the length of a longest cycle - of G can be expressed in terms of a certain graph parameter, and can be computed in polynomial time. Moreover, we show that G contains cycles of every length between 3 and the circumference, unless G is complete bipartite. If G is 1-tough then it is pancyclic or G = K-r,K-r with r = n/2. (C) 1997 John Wiley & Sons, Inc.

引用

页码：253 / 256

页数：4

共 50 条

[21] Sums of Powers of the Degrees of Graphs with k Cut Edges
Li, Shuchao
Yan, Lixia
GRAPHS AND COMBINATORICS, 2011, 27 (05) : 727 - 740
[22] Sums of Powers of the Degrees of Graphs with k Cut Edges
Shuchao Li
Lixia Yan
Graphs and Combinatorics, 2011, 27 : 727 - 740
[23] Cycle lengths in randomly perturbed graphs
Aigner-Horev, Elad
Hefetz, Dan
Krivelevich, Michael
RANDOM STRUCTURES & ALGORITHMS, 2023, 63 (04) : 867 - 884
[24] CYCLE LENGTHS AND CIRCUIT MATROIDS OF GRAPHS
WOODALL, DR
DISCRETE MATHEMATICS, 1992, 105 (1-3) : 269 - 273
[25] Degree and total degree of edges in bipolar fuzzy graphs with application
Borzooei, R. A.
Rashmanlou, Hossein
JOURNAL OF INTELLIGENT & FUZZY SYSTEMS, 2016, 30 (06) : 3271 - 3280
[26] Cycle lengths and chromatic number of graphs
Mihók, P
Schiermeyer, I
DISCRETE MATHEMATICS, 2004, 286 (1-2) : 147 - 149
[27] On arithmetic progressions of cycle lengths in graphs
Verstraëte, J
COMBINATORICS PROBABILITY & COMPUTING, 2000, 9 (04): : 369 - 373
[28] EXISTENCE OF GRAPHS WITH SPECIFIED CYCLE LENGTHS
MCCUAIG, W
DISCRETE MATHEMATICS, 1989, 78 (1-2) : 127 - 133
[29] Cycle lengths in sparse random graphs
Alon, Yahav
Krivelevich, Michael
Lubetzky, Eyal
RANDOM STRUCTURES & ALGORITHMS, 2022, 61 (03) : 444 - 461
[30] Number of edges in degree-magic graphs
Bezegova, L'udmila
Ivanco, Jaroslav
DISCRETE MATHEMATICS, 2013, 313 (12) : 1349 - 1357

← 1 2 3 4 5 →