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

##
###
On a conjecture of Gallai concerning complete subgraphs of k-critical graphs

1992
*
Discrete Mathematics
*

Zhou,

doi:10.1016/0012-365x(92)90642-s
fatcat:mllzaduwhrbw3lnqpdbisngqye
*On**a**conjecture**of**Gallai**concerning**complete**subgraphs**of**k*-*critical**graphs*, Discrete Mathematics 100 (1992) 223-228. ...*Gallai*asked whether each*k*-*critical**graph**of*order n contains at most n*complete**subgraphs**of*order*k*-1. ...*Gallai*raised the following problem: Is it true that every*k*-*critical**graph**of*order n contains at most it*complete**subgraphs**of*order*k*-l? ...##
###
Rainbow Generalizations of Ramsey Theory: A Survey

2010
*
Graphs and Combinatorics
*

In this work, we collect Ramsey-type results

doi:10.1007/s00373-010-0891-3
fatcat:ytvtt2g4hnhglbyx725xof43de
*concerning*rainbow and proper edge colorings*of**graphs*. Editions ... In slightly more generality,*one*could ask for any monochromatic*subgraph**of**a**k*-edge colored*complete**graph*. More formally, we have the following definition. ... Proof: By Theorem 75, the*Gallai*coloring*of**K*n is constructed by substituting*Gallai*colored*complete**graphs*into vertices*of**a*2-colored base*graph*. ...##
###
Page 4148 of Mathematical Reviews Vol. , Issue 93h
[page]

1993
*
Mathematical Reviews
*

[Zhou, Bing] (3-TREN)

*On**a**conjecture**of**Gallai**concerning**complete**subgraphs**of**k*-*critical**graphs*. ...*Gallai**conjectured*that every*k*-*critical**graph**on*n vertices contains at most n cliques*of*size*k*—1. The*conjecture*is trivially true for*k*< 3. M. ...##
###
Rainbow generalizations of Ramsey theory - a dynamic survey

2014
*
Theory and Applications of Graphs
*

In this work, we collect Ramsey-type results

doi:10.20429/tag.2014.000101
fatcat:zawfrrlt4jc4fbtiebsbpprsli
*concerning*rainbow edge colorings*of**graphs*. ... The authors*of*[68] also found the*Gallai*Ramsey numbers for all trees*of*order at most 6. Regarding paths in general, the following represents the best known bounds. ... Acknowledgement The authors would like to thank Maria Axenovich, Tao Jiang and the referee for helpful comments and corrections*on*the initial publication*of*this work. ...##
###
Inflations of anti-cycles and Hadwiger's Conjecture

2016
*
Journal of Combinatorics
*

Introduction Hadwiger's

doi:10.4310/joc.2016.v7.n2.a10
fatcat:gxgcb47unrh35jqjvsolufcxsi
*Conjecture*[9] from 1943 suggests*a*far reaching generalization*of*the Four Color Theorem, namely that any*k*-chromatic*graph*has the*complete**graph**K**k*as*a*minor. ... Then H is disconnected by*Gallai*[8] (Satz E 2 .1). and hence H consists*of*the join*of*two non-empty*critical**subgraphs*H 1 and H 2 . ... The proof, based*on*Hall's Theorem, is elementary, but not trivial. Our Theorems 2.1 and 2.6 can then be derived as corollaries*of*this lemma. ...##
###
Page 46 of Mathematical Reviews Vol. , Issue 80A
[page]

1980
*
Mathematical Reviews
*

The richest chapter is the

*one**on**complete**subgraphs*where for instance the result*of*Hajnal and Szemerédi*on*partitioning the vertices*of**a**graph**of*maximal degree*A*into (4+ 1) almost equicardinal independent ... In contrast to the linear growth rate*of*the maximum number*of**k*-blocks in*a*p-vertex*graph*, it is shown that the maximum number*of**critical**k*-vertex-connected*subgraphs**of*an ultrablock*of*connectivity ...##
###
On complete subgraphs of color-critical graphs

1995
*
Discrete Mathematics
*

*Gallai*

*conjectured*that every

*k*-

*critical*

*graph*

*of*order n contains at most n

*complete*(kl)-

*subgraphs*. ... In their paper, Abbott and Zhou asked the following question: is it true that the number

*of*

*complete*(

*k*-1)-

*subgraphs*

*of*any

*k*-

*critical*

*graph*G

*of*order n >

*k*is at most n -

*k*+ 3 (

*k*> 5)? ... Acknowledgement The author sincerely thanks

*one*

*of*the referees for providing the present proof

*of*Lemma 2, which is shorter than the original proof. ...

##
###
Triangle Packings and Transversals of Some $$K_{4}$$K4-Free Graphs

2018
*
Graphs and Combinatorics
*

Acknowledgements The author would like to thank the anonymous referees for valuable comments improving the structure

doi:10.1007/s00373-018-1903-y
fatcat:lssr3xle7vh35h2soo4ah4kw3u
*of*the paper and simplifying the proof*of*Theorem 13. ...*On*the other hand, the recognition*of**k*-*Gallai**graphs*remains*a*major open problem. Let us now translate Tuza's*Conjecture*in terms*of*the triangle*graph*. ... We then rely*on*the following result by*Gallai*(see [39] for*a*short proof and an extension): Theorem 14 (*Gallai*[13] ) If v is any vertex*of**a*connected θ-*critical**graph*G, then G has*a*minimum-size ...##
###
Page 2290 of Mathematical Reviews Vol. , Issue 87e
[page]

1987
*
Mathematical Reviews
*

(ie.

*a**subgraph**of**a**k*-tree) for small*k*. ... 87e:05051 orem*on*perfect*graphs*(1983) and Berge’s*conjectured*common generalization*of*the*Gallai*- Milgram and*Gallai*- Roy theorems. There are two slight problems with the revisions. ...##
###
Page 27 of Mathematical Reviews Vol. 49, Issue 1
[page]

1975
*
Mathematical Reviews
*

It was

*conjectured*by Griinbaum and Rao that if {d,} and {d,—*k*} are both graphical then there exists*a**graph*realizing {d,} that has*a*spanning regular*subgraph**of*degree*k*. ...*A*note*on*factor-*critical**graphs*. Studia Sci. Math. Hungar. '7 (1972), 279-280. ...##
###
Critically paintable, choosable or colorable graphs

2012
*
Discrete Mathematics
*

Using

doi:10.1016/j.disc.2012.07.035
fatcat:esfrt5d2qvarja6h7wobmklnai
*a*strong version*of*Brooks' Theorem, we generalize Gallai's Theorem about the structure*of*the low-degree*subgraph**of**critically**k*-colorable*graphs*, and introduce*a*more adequate lowest-degree*subgraph*... We also show that*on**a*fixed given surface, there are only finitely many*critically**k*-paintable/*k*-choosable/*k*-colorable*graphs*, if*k*≥ 6. ... Acknowledgments We want to thank the Abdus Salam School*of*Mathematical Sciences for providing*a*good research environment. ...##
###
Page 1323 of Mathematical Reviews Vol. , Issue 96c
[page]

1996
*
Mathematical Reviews
*

*Gallai*

*conjectured*that every

*k*-

*critical*

*graph*

*of*order n contains at most n

*complete*(

*k*— 1)-

*subgraphs*. ... In their paper, Abbott and Zhou asked the following question: Is it true that the number

*of*

*complete*(

*k*— 1)-

*subgraphs*

*of*any

*k*-

*critical*

*graph*G

*of*order n >

*k*is at most n —

*k*+3 (

*k*> 5)? ...

##
###
Page 2454 of Mathematical Reviews Vol. , Issue 94e
[page]

1994
*
Mathematical Reviews
*

*A*

*graph*G is

*k*-

*critical*if x(G) =

*k*and for every proper

*subgraph*H

*of*G, x(H) <

*k*, where x(G) is the chromatic number

*of*G. ... The author shows, by means

*of*an example, that

*a*

*conjecture*

*concerning*the Tutte polynomial

*of*

*a*

*graph*—namely that the coefficients form two-way unimodal sequences—is false. R. C. ...

##
###
On 4-critical planar graphs with high edge density

1991
*
Discrete Mathematics
*

Four problems

doi:10.1016/0012-365x(91)90039-5
fatcat:wolrqgixfjc5hkhd6oawnabqfm
*of*Grtinbaum*concerning*4-*critical*planar*graphs*with only vertices*of*valence higher than three are treated ... .,*On*4-*critical*planar*graphs*with high edge density, Discrete Mathematics 98 (1991) 147-151. ... An old*conjecture**of**Gallai*[2] that every 4-*critical*planar*graph*G contains e 5 2v -2 edges (that means d(G) d L d S c 2) was recently disproved by the present author [4] giving*a*4-*critical*planar ...##
###
On color critical graphs

1985
*
Journal of combinatorial theory. Series B (Print)
*

Denote by f(l,

doi:10.1016/0095-8956(85)90066-8
fatcat:opuk5us2gnhtfe7xa6czinsoyq
*k*, n) the largest positive integer such that any*k*-*critical**graph*with an vertices contains an Z-*critical**subgraph*with af(Z,*k*, n) vertices.*Conjecture*. ... The statement*concerning*the*graphs*Gk,, can be obtained easily from the Turin theorem. 1 THEOREM 1.4. If x(G) =*k*+ 1, x(G') = 1, G' is*a**subgraph**of*G, then II?(G) -E(G')I > t(*k*+ 1, I+ 1). ...
« Previous

*Showing results 1 — 15 out of 166 results*