Hamiltonicity and restricted degree conditions on induced subgraphs in claw-free graphs, II

Local connectivity, local degree conditions, some forbidden induced subgraphs, and cycle extendability

Discrete Mathematics ◽

10.1016/j.disc.2016.11.035 ◽

2017 ◽

Vol 340 (4) ◽

pp. 596-606

Author(s):

Christoph Brause ◽

Dieter Rautenbach ◽

Ingo Schiermeyer

Keyword(s):

Local Connectivity ◽

Induced Subgraphs ◽

Forbidden Induced Subgraphs ◽

Local Degree ◽

Degree Conditions ◽

Cycle Extendability

Hamiltonicity and restricted degree conditions on induced subgraphs in claw-free graphs

Discrete Mathematics ◽

10.1016/j.disc.2020.112165 ◽

2021 ◽

Vol 344 (1) ◽

pp. 112165

Author(s):

Zhi-Hong Chen

Keyword(s):

Induced Subgraphs ◽

Degree Conditions

Degree Conditions for k-Hamiltonian [a, b]-factors

Acta Mathematicae Applicatae Sinica English Series ◽

10.1007/s10255-021-1005-0 ◽

2021 ◽

Vol 37 (2) ◽

pp. 232-239

Author(s):

Jie Wu ◽

Si-zhong Zhou

Keyword(s):

Degree Conditions

Minimal classes of graphs of unbounded clique-width defined by finitely many forbidden induced subgraphs

Discrete Applied Mathematics ◽

10.1016/j.dam.2021.02.007 ◽

2021 ◽

Vol 295 ◽

pp. 57-69

Author(s):

A. Atminas ◽

R. Brignall ◽

V. Lozin ◽

J. Stacho

Keyword(s):

Induced Subgraphs ◽

Forbidden Induced Subgraphs

Excluding induced subgraphs: Critical graphs

Random Structures and Algorithms ◽

10.1002/rsa.20353 ◽

2010 ◽

Vol 38 (1-2) ◽

pp. 100-120 ◽

Cited By ~ 10

Author(s):

József Balogh ◽

Jane Butterfield

Keyword(s):

Induced Subgraphs ◽

Critical Graphs

Some Character Degree Conditions Implying Solvability of Finite Groups

Algebras and Representation Theory ◽

10.1007/s10468-011-9328-9 ◽

2011 ◽

Vol 16 (3) ◽

pp. 747-754 ◽

Cited By ~ 4

Author(s):

Kamal Aziziheris

Keyword(s):

Finite Groups ◽

Character Degree ◽

Degree Conditions

Degree and neighborhood intersection conditions restricted to induced subgraphs ensuring Hamiltonicity of graphs

Discrete Mathematics Algorithms and Applications ◽

10.1142/s1793830914500438 ◽

2014 ◽

Vol 06 (03) ◽

pp. 1450043

Author(s):

Bo Ning ◽

Shenggui Zhang ◽

Bing Chen

Keyword(s):

Hamilton Cycles ◽

Induced Subgraphs ◽

Degree Sum ◽

Degree Condition

Let claw be the graph K1,3. A graph G on n ≥ 3 vertices is called o-heavy if each induced claw of G has a pair of end-vertices with degree sum at least n, and called 1-heavy if at least one end-vertex of each induced claw of G has degree at least n/2. In this note, we show that every 2-connected o-heavy or 3-connected 1-heavy graph is Hamiltonian if we restrict Fan-type degree condition or neighborhood intersection condition to certain pairs of vertices in some small induced subgraphs of the graph. Our results improve or extend previous results of Broersma et al., Chen et al., Fan, Goodman and Hedetniemi, Gould and Jacobson, and Shi on the existence of Hamilton cycles in graphs.

Bounds for the b-chromatic Number of Induced Subgraphs and G − e

Algorithms and Discrete Applied Mathematics - Lecture Notes in Computer Science ◽

10.1007/978-3-319-14974-5_11 ◽

2015 ◽

pp. 111-116

Author(s):

P. Francis ◽

S. Francis Raj

Keyword(s):

Chromatic Number ◽

Induced Subgraphs

Induced subgraphs of graphs with large chromatic number. XI. Orientations

European Journal of Combinatorics ◽

10.1016/j.ejc.2018.09.003 ◽

2019 ◽

Vol 76 ◽

pp. 53-61 ◽

Cited By ~ 1

Author(s):

Maria Chudnovsky ◽

Alex Scott ◽

Paul Seymour

Keyword(s):

Chromatic Number ◽

Induced Subgraphs ◽

Large Chromatic Number

Large induced subgraphs with equated maximum degree

Discrete Mathematics ◽

10.1016/j.disc.2009.09.003 ◽

2010 ◽

Vol 310 (4) ◽

pp. 742-747 ◽

Cited By ~ 4

Author(s):

Y. Caro ◽

R. Yuster

Keyword(s):

Maximum Degree ◽

Induced Subgraphs