scholarly journals On the forbidden induced subgraph probe and sandwich problems

2018 ◽  
Vol 234 ◽  
pp. 56-66 ◽  
Author(s):  
Fernanda Couto ◽  
Luerbio Faria ◽  
Sylvain Gravier ◽  
Sulamita Klein
Keyword(s):  
Induced Subgraph ◽  
Forbidden Induced Subgraph

scholarly journals Classes of graphs with restricted interval models

1999 ◽  
Vol Vol. 3 no. 4 ◽  
Author(s):  
Andrzej Proskurowski ◽  
Jan Arne Telle
Keyword(s):  
Maximum Clique ◽  
Interval Graphs ◽  
Induced Subgraph ◽  
Graph Theoretic ◽  
Graph Classes ◽  
International Audience ◽  
Forbidden Induced Subgraph ◽  
Nested Hierarchy ◽  
Graph Families

International audience We introduce q-proper interval graphs as interval graphs with interval models in which no interval is properly contained in more than q other intervals, and also provide a forbidden induced subgraph characterization of this class of graphs. We initiate a graph-theoretic study of subgraphs of q-proper interval graphs with maximum clique size k+1 and give an equivalent characterization of these graphs by restricted path-decomposition. By allowing the parameter q to vary from 0 to k, we obtain a nested hierarchy of graph families, from graphs of bandwidth at most k to graphs of pathwidth at most k. Allowing both parameters to vary, we have an infinite lattice of graph classes ordered by containment.

scholarly journals Matrix Partitions with Finitely Many Obstructions

10.37236/976 ◽  
2007 ◽  
Vol 14 (1) ◽  
Author(s):  
Tomás Feder ◽  
Pavol Hell ◽  
Wing Xie
Keyword(s):  
Symmetric Matrix ◽  
Forbidden Subgraph ◽  
Input Graph ◽  
Induced Subgraphs ◽  
Induced Subgraph ◽  
Forbidden Induced Subgraphs ◽  
Extra Effort ◽  
Matrix Partition ◽  
Finite Set ◽  
Forbidden Induced Subgraph

Each $m$ by $m$ symmetric matrix $M$ over $0, 1, *$, defines a partition problem, in which an input graph $G$ is to be partitioned into $m$ parts with adjacencies governed by $M$, in the sense that two distinct vertices in (possibly equal) parts $i$ and $j$ are adjacent if $M(i,j)=1$, and nonadjacent if $M(i,j)=0$. (The entry $*$ implies no restriction.) We ask which matrix partition problems admit a characterization by a finite set of forbidden induced subgraphs. We prove that matrices containing a certain two by two diagonal submatrix $S$ never have such characterizations. We then develop a recursive technique that allows us (with some extra effort) to verify that matrices without $S$ of size five or less always have a finite forbidden induced subgraph characterization. However, we exhibit a six by six matrix without $S$ which cannot be characterized by finitely many induced subgraphs. We also explore the connection between finite forbidden subgraph characterizations and related questions on the descriptive and computational complexity of matrix partition problems.

scholarly journals A forbidden induced subgraph characterization of distance-hereditary 5-leaf powers

2009 ◽  
Vol 309 (12) ◽  
pp. 3843-3852 ◽  
Author(s):  
Andreas Brandstädt ◽  
Van Bang Le ◽  
Dieter Rautenbach
Keyword(s):  
Induced Subgraph ◽  
Forbidden Induced Subgraph

Forbidden induced subgraph characterization of cograph contractions

2004 ◽  
Vol 46 (3) ◽  
pp. 217-226 ◽  
Author(s):  
Igor Ed. Zverovich ◽  
Inessa I. Zverovich
Keyword(s):  
Induced Subgraph ◽  
Forbidden Induced Subgraph

Requiring adjacent chords in cycles

2018 ◽  
Vol 10 (01) ◽  
pp. 1850003
Author(s):  
Terry A. McKee
Keyword(s):  
Induced Subgraph ◽  
New Class ◽  
Forbidden Induced Subgraph

Define a new class of graphs by cycles of length 5 or more always having adjacent chords. This is equivalent to cycles of length 5 or more always having noncrossing chords, which is a property that has a known forbidden induced subgraph characterization. Another characterization comes from viewing the graphs in this class in contrast to distance-hereditary graphs (which are characterized by cycles of length 5 or more always having crossing chords). Moreover, the graphs in the new class are those in which every edge of every cycle [Formula: see text] of length 5 or more forms a triangle with a third vertex of [Formula: see text] (generalizing that a graph is chordal if and only if every edge of every cycle [Formula: see text] of length 4 or more forms a triangle with a third vertex of [Formula: see text]). This leads to a strategically-required subgraph characterization of the new class.

scholarly journals On the forbidden induced subgraph sandwich problem

2011 ◽  
Vol 159 (16) ◽  
pp. 1717-1725 ◽  
Author(s):  
Simone Dantas ◽  
Celina M.H. de Figueiredo ◽  
Murilo V.G. da Silva ◽  
Rafael B. Teixeira
Keyword(s):  
Induced Subgraph ◽  
Forbidden Induced Subgraph

scholarly journals A General Method for Forbidden Induced Subgraph Sandwich Problem NP-completeness

2019 ◽  
Vol 346 ◽  
pp. 393-400
Author(s):  
Simone Dantas ◽  
Celina M.H. de Figueiredo ◽  
Priscila Petito ◽  
Rafael B. Teixeira
Keyword(s):  
Induced Subgraph ◽  
Np Completeness ◽  
Forbidden Induced Subgraph ◽  
General Method

scholarly journals On Betti numbers of flag complexes with forbidden induced subgraphs

2019 ◽  
Vol 168 (3) ◽  
pp. 567-600
Author(s):  
KARIM ADIPRASITO ◽  
ERAN NEVO ◽  
MARTIN TANCER
Keyword(s):  
Growth Rate ◽  
Betti Number ◽  
Betti Numbers ◽  
Interesting Case ◽  
Induced Subgraphs ◽  
Induced Subgraph ◽  
Theorem Of The Alternative ◽  
Forbidden Induced Subgraphs ◽  
Forbidden Induced Subgraph ◽  
Flag Complexes

AbstractWe analyse the asymptotic extremal growth rate of the Betti numbers of clique complexes of graphs on n vertices not containing a fixed forbidden induced subgraph H.In particular, we prove a theorem of the alternative: for any H the growth rate achieves exactly one of five possible exponentials, that is, independent of the field of coefficients, the nth root of the maximal total Betti number over n-vertex graphs with no induced copy of H has a limit, as n tends to infinity, and, ranging over all H, exactly five different limits are attained.For the interesting case where H is the 4-cycle, the above limit is 1, and we prove a superpolynomial upper bound.

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