منابع مشابه
Cycle transversals in bounded degree graphs
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We introduce and discuss generalizations of the problem of independent transversals. Given a graph property R, we investigate whether any graph of maximum degree at most d with a vertex partition into classes of size at least p admits a transversal having property R. In this paper we study this problem for the following properties R: “acyclic”, “H-free”, and “having connected components of orde...
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Transversals in r-partite graphs with various properties are known to have many applications in graph theory and theoretical computer science. We investigate f -bounded transversals (or f -BT), that is, transversals whose connected components have order at most f . In some sense we search for the the sparsest f -BT-free graphs. We obtain estimates on the smallest maximum degree that 3-partite a...
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A cycle-transversal of a graph G is a subset T ⊆ V (G) such that T ∩V (C) 6= ∅ for every cycle C of G. A clique cycle-transversal, or cct for short, is a cycle-transversal which is a clique. Recognizing graphs which admit a cct can be done in polynomial time; however, no structural characterization of such graphs is known. We characterize distancehereditary graphs admitting a cct in terms of fo...
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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: Electronic Notes in Discrete Mathematics
سال: 2009
ISSN: 1571-0653
DOI: 10.1016/j.endm.2009.11.032