Ramsey graphs contain many distinct induced subgraphs

1991 ◽  
Vol 7 (1) ◽  
pp. 1-6 ◽  
Author(s):  
N. Alon ◽  
A. Hajnal
Keyword(s):  
Induced Subgraphs ◽  
Ramsey Graphs

Sizes of Induced Subgraphs of Ramsey Graphs

2009 ◽  
Vol 18 (4) ◽  
pp. 459-476 ◽  
Author(s):  
NOGA ALON ◽  
JÓZSEF BALOGH ◽  
ALEXANDR KOSTOCHKA ◽  
WOJCIECH SAMOTIJ
Keyword(s):  
Lower Bound ◽  
Induced Subgraphs ◽  
Induced Subgraph ◽  
Vertex Graph ◽  
Ramsey Graphs

An n-vertex graph G is c-Ramsey if it contains neither a complete nor an empty induced subgraph of size greater than c log n. Erdős, Faudree and Sós conjectured that every c-Ramsey graph with n vertices contains Ω(n5/2) induced subgraphs, any two of which differ either in the number of vertices or in the number of edges, i.e., the number of distinct pairs (|V(H)|, |E(H)|), as H ranges over all induced subgraphs of G, is Ω(n5/2). We prove an Ω(n2.3693) lower bound.

scholarly journals Proof of a conjecture on induced subgraphs of Ramsey graphs

2018 ◽  
Vol 372 (8) ◽  
pp. 5571-5594
Author(s):  
Matthew Kwan ◽  
Benny Sudakov
Keyword(s):  
Induced Subgraphs ◽  
Ramsey Graphs

Excluding induced subgraphs: Critical graphs

2010 ◽  
Vol 38 (1-2) ◽  
pp. 100-120 ◽  
Author(s):  
József Balogh ◽  
Jane Butterfield
Keyword(s):  
Induced Subgraphs ◽  
Critical Graphs

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

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.

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

2019 ◽  
Vol 76 ◽  
pp. 53-61 ◽  
Author(s):  
Maria Chudnovsky ◽  
Alex Scott ◽  
Paul Seymour
Keyword(s):  
Chromatic Number ◽  
Induced Subgraphs ◽  
Large Chromatic Number

scholarly journals Large induced subgraphs with equated maximum degree

2010 ◽  
Vol 310 (4) ◽  
pp. 742-747 ◽  
Author(s):  
Y. Caro ◽  
R. Yuster
Keyword(s):  
Maximum Degree ◽  
Induced Subgraphs
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