A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
Vertex Colouring and Forbidden Subgraphs ? A Survey

2004
*
Graphs and Combinatorics
*

*À*µ ÑÔÐ × Ò Ó × ÖÚ Ø ÓÒº ËØ ÖØ Ò Û Ø

*À*½ ¸Ø ÓÑÔÐ Ñ ÒØ Ó Ø ¹ Ý Ð ¸Û ¬Ò

*À*·½

*À*¸Ø Î ÖØ Ü ÓÐÓÙÖ Ò Ò ÓÖ Ò ×Ù Ö Ô × ½½ Ð Ü Ó Ö Ô ÔÖÓ Ù Ø Ó Ø Ö Ô × Ò

*À*º

*À*Ö ¸Ø Ð Ü Ó Ö Ô ÔÖÓ ¹ Ù Ø Ó ØÛÓ Ö Ô × Ò

*À*× Ø Ö Ô

*À*... Ï Ø «´ µ ¾ Û Ø Ò Ó × ÖÚ Ø Ø Ú ÖÝ ÓÐÓÙÖ Ó ÓÐÓÙÖ Ò Ó

*À*·½ ÔÔ Ö× Ò Ø ÑÓ×Ø ØÛÓ « Ö ÒØ ÓÔ × Ó

*À*º

*À*Ò ¸

*À*× Ø ÓÖ Ö Ò´

*À*µ ¸ Ò Ô Ò Ò ÒÙÑ Ö «´

*À*µ ¾ Ò Ð ÕÙ ÒÙÑ Ö ´

*À*µ ¿ º Ì Ö ÓÖ ¸ Ø× ÖÓÑ Ø ÒÙÑ Ö ´

*À*µ × Ø Ð ×Ǿ ¾µ ...

##
###
Reconfiguration of vertex colouring and forbidden induced subgraphs
[article]

2022
*
arXiv
*
pre-print

In this paper, we investigate the connectivity

arXiv:2206.09268v2
fatcat:xsxdkirhd5gilk7pj4z7m3soou
*and*diameter of ℛ_k+1(G) for*a*k-*colourable*graph G restricted by*forbidden*induced*subgraphs*. ... The reconfiguration graph of the k-*colourings*, denoted ℛ_k(G), is the graph whose vertices are the k-*colourings*of G*and*two*colourings*are adjacent in ℛ_k(G) if they differ in*colour*on exactly one*vertex*... The connectivity*and*diameter of R ℓ (G) has also been investigated for classes of graphs defined by more than one*forbidden*induced*subgraph*. ...##
###
A Survey on the Computational Complexity of Colouring Graphs with Forbidden Subgraphs
[article]

2016
*
arXiv
*
pre-print

We

arXiv:1407.1482v8
fatcat:bjkwvdxmszgmnotdrv53epjt54
*survey*known results on the computational complexity of*Colouring**and*k-*Colouring*for graph classes that are characterized by one or two*forbidden*induced*subgraphs*. ... We also consider*a*number of variants: for example, where the problem is to extend*a*partial*colouring*, or where lists of permissible*colours*are given for each*vertex*. ... We thank Konrad Dabrowski, François Dross, Oliver Schaudt*and*two anonymous reviewers for helpful comments. ...##
###
A survey of hereditary properties of graphs

1997
*
Discussiones Mathematicae Graph Theory
*

In this paper we

doi:10.7151/dmgt.1037
fatcat:qpxm2z2i6rhwra7lk42p2lg2au
*survey*results*and*open problems on the structure of additive*and*hereditary properties of graphs. ... The important role of*vertex*partition problems, in particular the existence of uniquely partitionable graphs*and*reducible properties of graphs in this structure, is emphasized. ... The Choice Number Let G be*a*graph*and*let L(v) be*a*list of*colours*(say, positive integers) prescribed for the*vertex*v,*and*P ∈ M . ...##
###
A survey of χ-boundedness
[article]

2020
*
arXiv
*
pre-print

If

arXiv:1812.07500v3
fatcat:q3xjtgcmkfh7fdzq2gnidx7lri
*a*graph has bounded clique number,*and*sufficiently large chromatic number, what can we say about its induced*subgraphs*? ... This is*a**survey*of where we are now. ... We would particularly like to thank Pierre Aboulker, Pierre Charbit, Louis Esperet, Patrice Ossona de Mendez, Sang-Il Oum, Bruce Reed, Vaidy Sivaraman, Sophie Spirkl*and*Nicolas Trotignon. ...##
###
Reflexive cacti: A survey

2016
*
Applicable Analysis and Discrete Mathematics
*

*A*graph is called reflexive if its second largest eigenvalue does not exceed 2. We

*survey*the results on reflexive cacti obtained in the last two decades. ... We also discuss various patterns of appearing of Smith graphs as

*subgraphs*of reflexive cacti. ... The authors are grateful to the Serbian Ministry of Education, Science

*and*Technological Development for financial support through Projects No 174033

*and*174012. ...

##
###
A Survey on the Computational Complexity of Coloring Graphs with Forbidden Subgraphs

2016
*
Journal of Graph Theory
*

We

doi:10.1002/jgt.22028
fatcat:mv5j3zmgjjfkhij5inlnbxdxhy
*survey*known results on the computational complexity of*COLOURING**and*k-*COLOURING*for graph classes that are characterized by one or two*forbidden*induced*subgraphs*. ... 2016) '*A**survey*on the computational complexity of coloring graphs with*forbidden**subgraphs*.', Journal of graph theory. . ... We thank Konrad Dabrowski, François Dross, Oliver Schaudt*and*two anonymous reviewers for helpful comments. ...##
###
Simplicial decompositions of graphs: a survey of applications

1989
*
Discrete Mathematics
*

We

doi:10.1016/0012-365x(89)90084-8
fatcat:n7g4dykpxnahzogrtopyf2nitq
*survey*applications of simplicial decompositions (decompositions by separating complete*subgraphs*) to problems in graph theory. ... of B, to*a*given k-*colouring*of S,,*and*hence to any given k-*colouring*of GI, := l_l*__ Bh; thus by induction, G can be k-*coloured*if every Bh can. ...##
###
Reconfiguration of Colourings and Dominating Sets in Graphs: a Survey
[article]

2020
*
arXiv
*
pre-print

We

arXiv:2003.05956v1
fatcat:b2akpiblpvg6zk3n55ydlcp64y
*survey*results concerning reconfigurations of*colourings**and*dominating sets in graphs. ... The vertices of the k-*colouring*graph C_k(G) of*a*graph G correspond to the proper k-*colourings*of*a*graph G, with two k-*colourings*being adjacent whenever they differ in the*colour*of exactly one*vertex*... ; • C 3 , C 4 , C 6 are the only cycles that are*colouring*graphs; • every tree is*a**subgraph*of*a**colouring*graph (thus there is no finite*forbidden**subgraph*characterisation of*colouring*graphs). ...##
###
A survey on enhanced power graphs of finite groups

2022
*
Electronic Journal of Graph Theory and Applications
*

We

doi:10.5614/ejgta.2022.10.1.6
fatcat:r6p6q6ckebc6dbpcvxiorct4ay
*survey*known results on enhanced power graphs of finite groups. Open problems, questions*and*suggestions for future work are also included. ...*Forbidden**subgraphs*in the enhanced power graph This section contains the results on the*forbidden**subgraphs*of enhanced power graphs. ... Section 5 is devoted to the*forbidden**subgraphs*of enhanced power graphs. ...##
###
Generalizations of tournaments: A survey

1998
*
Journal of Graph Theory
*

We

doi:10.1002/(sici)1097-0118(199808)28:4<171::aid-jgt1>3.0.co;2-g
fatcat:urwonpylavfwzelzhggoojzk74
*survey*results concerning various generalizations of tournaments. The reader will see that tournaments are by no means the only class of directed graphs with*a*very rich structure. ... We describe, among numerous other topics mostly related to paths*and*cycles, results on hamiltonian paths*and*cycles. ... In [81]*a*characterization was given in terms of intersection graphs*and**a*characterization by*forbidden*induced*subgraphs*was described. ...##
###
Cycles and paths in semicomplete multipartite digraphs, theorems, and algorithms: a survey

1995
*
Journal of Graph Theory
*

We describe results (theorems

doi:10.1002/jgt.3190190405
fatcat:7cnx4wtlobhcnjizv3ry7lnszi
*and*algorithms) on directed walks in semicomplete m-partite digraphs including some recent results concerning tournaments. ...*A*digraph obtained by replacing each edge of*a*complete m-partite graph by an arc or*a*pair of mutually opposite arcs with the same end vertices is called*a*semicomplete m-partite digraph. ... In particular, they proved that every tournament whose arcs are*coloured*with two*colours*contains*a**vertex*v such that for every other*vertex*w there exists*a*monochromatic (v, w)-path. ...##
###
A survey on integral graphs

2002
*
Publikacija Elektrotehnickog fakulteta - serija matematika
*

*A*graph whose spectrum consists entirely of integers is called an integral graph. We present

*a*

*survey*of results on integral graphs

*and*on the corresponding proof techniques. ... Notice that any

*subgraph*of H, together with the induced labelling, produces an induced

*subgraph*of G. ... ,n/k , on n vertices

*and*k

*colour*classes of sizes n/k, is always integral; the eigenvalues are: n − n/k, 0 n−k , (−n/k) k−1 . ...

##
###
On some intriguing problems in hamiltonian graph theory—a survey

2002
*
Discrete Mathematics
*

We

doi:10.1016/s0012-365x(01)00325-9
fatcat:wcggfjuntbgrjmegqldzdz55hy
*survey*results*and*open problems in hamiltonian graph theory centered around three themes: regular graphs, t-tough graphs,*and*claw-free graphs. ... Introduction As this*survey*paper is the outcome of an invited lecture at the eighth Workshop on Cycles*and**Colourings*(StarÃ*a*LesnÃ*a*, Slovakia, 1999), the presentation of results is motivated by open ... Most of these results involve su cient conditions in terms of degrees, neighborhoods,*forbidden**subgraphs*or (local) connectivity. ...##
###
A Survey of Forbidden Configuration Results

2013
*
Electronic Journal of Combinatorics
*

Or alternatively if $

doi:10.37236/2379
fatcat:wxikdxtrqfbqxbdlbpc2dypuyu
*A*$ is an $m\times (\hbox{forb}(m,F)+1)$ simple matrix then $*A*$ has*a*submatrix which is*a*row*and*column permutation of $F$. We call $F$*a**forbidden*configuration. ... Let $F$ be*a*$k\times \ell$ (0,1)-matrix. We say*a*(0,1)-matrix $*A*$ has $F$ as*a*configuration if there is*a*submatrix of $*A*$ which is*a*row*and*column permutation of $F$. ... The investigations into the extremal problem of the maximum number of edges in an n*vertex*graph with no*subgraph*H originated with Erdős*and*Stone [ES46]*and*Simonovits [ES66]*and*has*a*large*and*...
« Previous

*Showing results 1 — 15 out of 547 results*