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## Filters

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Colorful induced subgraphs

1992
*
Discrete Mathematics
*

*Colorful*

*induced*

*subgraphs*, Discrete Mathematics 101 (1992) 165-169. A

*colored*graph is a graph whose vertices have been properly, though not necessarily optimally

*colored*, with integers. ... A

*subgraph*of a

*colored*graph is

*colorful*if each of its vertices has a distinct

*color*. ... The

*colored*

*subgraph*(subdigraph) of G

*induced*by H is G[H] = (V, E', f '), where (V, E') is the

*subgraph*(subdigraph) of (V, E)

*induced*by H and f' is f restricted to H. ...

##
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Rainbow induced subgraphs in proper vertex colorings
[article]

2011
*
arXiv
*
pre-print

For a given graph H we define ρ(H) to be the minimum order of a graph G such that every proper vertex

arXiv:1105.3712v1
fatcat:ai2j75cgtndi5ghsoukxnu5zsu
*coloring*of G contains a rainbow*induced**subgraph*isomorphic to H. ... This research is motivated by some ideas in on-line graph*coloring*algorithms. ... In this paper we deal with proper vertex*colorings*of graphs,*colorings*, in short, and rainbow*induced**subgraphs*, by which we mean*induced**subgraphs*whose all vertices have different*colors*. ...##
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Avoiding rainbow induced subgraphs in vertex-colorings
[article]

2016
*
arXiv
*
pre-print

For a fixed graph H on k vertices, and a graph G on at least k vertices, we write G→ H if in any vertex-

arXiv:1605.06172v1
fatcat:wqby2wraineb5n5dlnqlg65xfe
*coloring*of G with k*colors*, there is an*induced**subgraph*isomorphic to H whose vertices have distinct ... This determines the*induced*vertex-anti-Ramsey number for all graphs and shows that totally multicolored*induced**subgraphs*are, in most cases, easily avoidable. ... of R t (H) are*colored*with t*colors*, then there is an*induced**subgraph*of R t (H) isomorphic to H which is monochromatic. ...##
###
Complexity dichotomy for List-5-Coloring with a forbidden induced subgraph
[article]

2021
*
arXiv
*
pre-print

Also, we say G is H-free if H is not isomorphic to an

arXiv:2105.01787v2
fatcat:be63sbjvhbfjjdhxt2mvk4el2y
*induced**subgraph*of G. We use P_t to denote the path on t vertices. ... restricted to H-free graphs can be solved in polynomial time if and only if H is an*induced**subgraph*of either rP_3 or P_5+rP_1 for some positive integer r. ... If H is an*induced**subgraph*of rP 3 , then the result follows from Theorem 14, and if H is an*induced**subgraph*of P 5 + rP 1 , then the result follows from Theorem 7. ...##
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Avoiding Rainbow Induced Subgraphs in Vertex-Colorings

2008
*
Electronic Journal of Combinatorics
*

For a fixed graph $H$ on $k$ vertices, and a graph $G$ on at least $k$ vertices, we write $G\longrightarrow H$ if in any vertex-

doi:10.37236/736
fatcat:3lnbwdgxifgjjmbdrb7ef7ewwy
*coloring*of $G$ with $k$*colors*, there is an*induced**subgraph*isomorphic ... This determines the*induced*vertex-anti-Ramsey number for all graphs and shows that totally multicolored*induced**subgraphs*are, in most cases, easily avoidable. ... of R t (H) are*colored*with t*colors*, then there is an*induced**subgraph*of R t (H) isomorphic to H which is monochromatic. ...##
###
On the complexity of finding large odd induced subgraphs and odd colorings
[article]

2021
*
arXiv
*
pre-print

We study the complexity of the problems of finding, given a graph G, a largest

arXiv:2002.06078v2
fatcat:kqtwnbdf45h37fszgz2baxzlsm
*induced**subgraph*of G with all degrees odd (called an odd*subgraph*), and the smallest number of odd*subgraphs*that partition ... Now note that every proper vertex*coloring*of G using q*colors*can be lifted to a partition of V (G) into q odd*induced**subgraphs*(in fact, odd*induced*forests). ... Tight bounds In this section we provide two tight bounds concerning odd*induced**subgraphs*and odd*colorings*. ...##
###
Complexity of Coloring Graphs without Forbidden Induced Subgraphs
[chapter]

2001
*
Lecture Notes in Computer Science
*

We further initiate a study of this problem for two forbidden

doi:10.1007/3-540-45477-2_23
fatcat:bykjq7v4tjbg5jzuyaxlh7y6ly
*subgraphs*. ... We give a complete characterization of parameter graphs H for which the problem of*coloring*H-free graphs is polynomial and for which it is NP-complete. ... If H is an*induced**subgraph*of H then every H-free graph is also H -free, and hence H-Free*Coloring*∝ H -Free*Coloring*. ...##
###
Forbidden Induced Subgraph Of The Comparability Graph And Three Colored Posets

2018
*
Zenodo
*

As a continuation of the study of 3-

doi:10.5281/zenodo.1412751
fatcat:4vkdjxz73jhoti2woxkarnpsym
*colored*diagrams we characterize some forbidden ⊲ - preserving subposets of the posets whose cover-incomparability graph contains one of the forbidden*induced**subgraph*... We call posets having the above mentioned diagrams as 3-*colored*diagrams. Let F (G) be a collection of forbidden*induced**subgraphs*. ... FIGURE 1 : 1 Families of forbidden*induced**subgraphs*for comparability graph [14] Figure 2 : 2 Forbidden 3-*colored*diagrams for posets whose C-I graphs contains depicted inFigure 1(c). ...##
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Parameterized Algorithms for Max Colorable Induced Subgraph Problem on Perfect Graphs

2018
*
Algorithmica
*

We address the parameterized complexity of Max

doi:10.1007/s00453-018-0431-8
fatcat:2zlvhsjwozbyrjt3lezhobrdyy
*Colorable**Induced**Subgraph*on perfect graphs. The problem asks for a maximum sized q-*colorable**induced**subgraph*of an input graph G. ... -The second algorithm runs in time q +o( ) n O(1) Tα where Tα is the time required to find a maximum independent set in any*induced**subgraph*of G. ... An interesting direction of research that this paper opens up is the study of parameterized complexity of*Induced**Subgraph*Isomorphism on special graph classes. ...##
###
Parameterized Algorithms for Max Colorable Induced Subgraph Problem on Perfect Graphs
[chapter]

2013
*
Lecture Notes in Computer Science
*

We address the parameterized complexity of Max

doi:10.1007/978-3-642-45043-3_32
fatcat:tyxfpsbqm5bgdcrzzgdmjuiqea
*Colorable**Induced**Subgraph*on perfect graphs. The problem asks for a maximum sized q-*colorable**induced**subgraph*of an input graph G. ... -The second algorithm runs in time q +o( ) n O(1) Tα where Tα is the time required to find a maximum independent set in any*induced**subgraph*of G. ... An interesting direction of research that this paper opens up is the study of parameterized complexity of*Induced**Subgraph*Isomorphism on special graph classes. ...##
###
The complexity of the 3-colorability problem in the absence of a pair of small forbidden induced subgraphs

2015
*
Discrete Mathematics
*

We completely determine the complexity status of the 3-

doi:10.1016/j.disc.2015.04.019
fatcat:5kklqcsohbauvg2c543a42bfve
*colorability*problem for hereditary graph classes defined by two forbidden*induced**subgraphs*with at most five vertices. ... If it exists, then G is 3-*colorable*if and only if N(x)*induces*a bipartite*subgraph*. Hence, we have a polynomial-time reduction. ... If there are at least two nonempty sets, then each of them*induces*a complete*subgraph*. ...##
###
Some perfect coloring properties of graphs

1979
*
Journal of combinatorial theory. Series B (Print)
*

Notice that for positive integers n a graph G has a complete n-

doi:10.1016/0095-8956(79)90067-4
fatcat:hvrz35tav5gxjj5giack7lud5a
*coloring*if every finite*induced**subgraph*H of G has one. Now let H be an arbitrary*induced**subgraph*of G which satisfies (8). ... Hence, if G is yx-perfect, it does not contain an*induced**subgraph*isomo.rphic to P4. (3) =+-(1) Suppose G does not contain an*induced**subgraph*isomorphic to P4, and let c be a Grundy y(G)-*coloring*of ...##
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A Characterization of 2-Tree Proper Interval 3-Graphs

2014
*
Journal of Discrete Mathematics
*

We characterize the class of 2-trees which are interval 3-graphs via a list of three graphs and three infinite families of forbidden

doi:10.1155/2014/143809
fatcat:443temg6rzaphmfe4na5qeqeiy
*induced**subgraphs*. ... An intervalp-graph is the intersection graph of a collection of intervals which have been*colored*withpdifferent*colors*with edges corresponding to nonempty intersection of intervals from different*color*... Since −1 and +1 are the same*color*, must be odd for all . If = 1 then from Figure 6 is an*induced*Figure 6 is an*induced**subgraph*of { −1 , , +1 , 1 , . . . , } with 1 ≅ . ...##
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On Subgraphs Induced by Transversals in Vertex-Partitions of Graphs

2006
*
Electronic Journal of Combinatorics
*

If $H\notin {\cal F}$, then for any graph $G$ on at least $4k-1$ vertices, there is a $k$-

doi:10.37236/1062
fatcat:53bjbicfknfard2nf2bbzilkze
*coloring*of vertices of $G$ avoiding totally multicolored*induced**subgraphs*isomorphic to $H$. ... For a fixed graph $H$ on $k$ vertices, we investigate the graphs, $G$, such that for any partition of the vertices of $G$ into $k$*color*classes, there is a transversal of that partition*inducing*$H$. ... any vertex-*coloring*of G with fixed number of*colors*, there is an*induced*monochromatic*subgraph*isomorphic to H? ...##
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A note on the Cornaz–Jost transformation to solve the graph coloring problem

2013
*
Information Processing Letters
*

In this note, we use a reduction by Cornaz and Jost from the graph (max-)

doi:10.1016/j.ipl.2013.05.014
fatcat:xhfsquekyfhrdkeactdhkqn56a
*coloring*problem to the maximum (weighted) stable set problem in order to characterize new graph classes where the graph*coloring*... problem and the more general max-*coloring*problem can be solved in polynomial time. ... If G has an odd hole as*induced**subgraph*then T (G) has a hole of length 5 as*induced**subgraph*, and if G has an odd antihole C k as*induced**subgraph*then T (G) has an odd hole C k as*induced**subgraph*. ...
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