منابع مشابه
Outerstring graphs are chi-bounded
An outerstring graph is an intersection graph of curves lying in a halfplane with one endpoint on the boundary of the halfplane. It is proved that the outerstring graphs are χ-bounded, that is, their chromatic number is bounded by a function of their clique number. This generalizes a series of previous results on χ-boundedness of outerstring graphs with various restrictions of the shape of the ...
متن کامل$\chi$-bounded families of oriented graphs
A famous conjecture of Gyárfás and Sumner states for any tree T and integer k, if the chromatic number of a graph is large enough, either the graph contains a clique of size k or it contains T as an induced subgraph. We discuss some results and open problems about extensions of this conjecture to oriented graphs. We conjecture that for every oriented star S and integer k, if the chromatic numbe...
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We obtain a number of lower bounds on the running time of algorithms solving problems on graphs of bounded treewidth. We prove the results under the Strong Exponential Time Hypothesis of Impagliazzo and Paturi. In particular, assuming that SAT cannot be solved in (2−ǫ)m time, we show that for any ǫ > 0; • INDEPENDENT SET cannot be solved in (2 − ǫ)tw(G)|V (G)| time, • DOMINATING SET cannot be s...
متن کاملClasses of graphs with small rank decompositions are X-bounded
A class of graphs G is χ-bounded if the chromatic number of graphs in G is bounded by a function of the clique number. We show that if a class G is χ-bounded, then every class of graphs admitting a decomposition along cuts of small rank to graphs from G is χ-bounded. As a corollary, we obtain that every class of graphs with bounded rank-width (or equivalently, clique-width) is χ-bounded.
متن کاملk-forested choosability of graphs with bounded maximum average degree
A proper vertex coloring of a simple graph is $k$-forested if the graph induced by the vertices of any two color classes is a forest with maximum degree less than $k$. A graph is $k$-forested $q$-choosable if for a given list of $q$ colors associated with each vertex $v$, there exists a $k$-forested coloring of $G$ such that each vertex receives a color from its own list. In this paper, we prov...
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ژورنال
عنوان ژورنال: SIAM Journal on Discrete Mathematics
سال: 2019
ISSN: 0895-4801,1095-7146
DOI: 10.1137/17m1157374