Frantisek Kardos

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A subset S of vertices of a graph G is called a k-path vertex cover if every path of order k in G contains at least one vertex from S. Denote by ψk(G) the minimum cardinality of a k-path vertex cover in G. It is shown that the problem of determining ψk(G) is NP-hard for each k ≥ 2, while for trees the problem can be solved in linear time. We investigate(More)
We show that for every cubic graph G with sufficiently large girth there exists a probability distribution on edge-cuts of G such that each edge is in a randomly chosen cut with probability at least 0.88672. This implies that G contains an edge-cut of size at least 1.33008n, where n is the number of vertices of G, and has fractional cut covering number at(More)
In this paper, we study cyclic edge-cuts in fullerene graphs. First, we show that the cyclic edge-cuts of a fullerene graph can be constructed from its trivial cyclic 5and 6-edge-cuts using three basic operations. This result immediatelly implies the fact that fullerene graphs are cyclically 5-edge-connected. Next, we characterize a class of nanotubes as(More)
We show that every (sub)cubic n-vertex graph with sufficiently large girth has fractional chromatic number at most 2.2978 which implies that it contains an independent set of size at least 0.4352n. Our bound on the independence number is valid to random cubic graphs as well as it improves existing lower bounds on the maximum cut in cubic graphs with large(More)
The dissociation number of a graph G is the number of vertices in a maximum size induced subgraph of G with vertex degree at most 1. A k-path vertex cover of a graph G is a subset S of vertices of G such that every path of order k in G contains at least one vertex from S. The minimum 3-path vertex cover is a dual problem to the dissociation number. For this(More)