# Tomás Madaras

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• Discussiones Mathematicae Graph Theory
• 1996
A subgraph of a plane graph is light if the sum of the degrees of the vertices of the subgraph in the graph is small. It is well known that a plane graph of minimum degree five contains light edges and light triangles. In this paper we show that every plane graph of minimum degree five contains also light stars K1,3 and K1,4 and a light 4-path P4. The(More)
• Discrete Mathematics
• 2007
A graph is called 1-planar if it can be drawn in the plane so that each its edge is crossed by at most one other edge. In the paper, we study the existence of subgraphs of bounded degrees in 1-planar graphs. It is shown that each 1-planar graph contains a vertex of degree at most 7; we also prove that each 3-connected 1-planar graph contains an edge with(More)
• Discussiones Mathematicae Graph Theory
• 2009
A graph is 1-planar if it can be embedded in the plane so that each edge is crossed by at most one other edge. We prove that each 1-planar graph of minimum degree 5 and girth 4 contains (1) a 5-vertex adjacent to an ≤ 6-vertex, (2) a 4-cycle whose every vertex has degree at most 9, (3) a K1,4 with all vertices having degree at most 11.
• Bulletin of the World Health Organization
• 1995
Annual epidemics of bacillary dysentery have been a public health problem in Burundi for the last 14 years. Recent civil unrest, resulting in the displacement of large numbers of people into refugee settlements, has aggravated the situation. We report the results of a nationwide, health-centre based, sentinel site survey to check the drug resistance of(More)
The weight of a path in a graph is defined to be the sum of degrees of its vertices in entire graph. It is proved that each plane triangulation of minimum degree 5 contains a path P5 on 5 vertices of weight at most 29, the bound being precise, and each plane triangulation of minimum degree 4 contains a path P4 on 4 vertices of weight at most 31.
SETTING The pilot projects for tuberculosis (TB) control, supported by the World Health Organization (WHO) and based on the WHO recommended control strategy, directly-observed treatment, short-course (DOTS) in the Caucasian countries (Armenia, Azerbaijan, Georgia). OBJECTIVE To evaluate the results 2 years after the implementation of the pilot projects.(More)
• Discrete Mathematics
• 1999
A subgraph of a plane graph is light if each of its vertices has a small degree in the entire graph. Consider the class ~¢-(5) of plane triangulations of minimum degree 5. It is known that each G C,Y-(5) contains a light triangle. From a recent result of Jendrol' and Madaras the existence of light cycles C4 and C5 in each G C.~(5) follows. We prove here(More)
A subgraph of a plane graph is light if the sum of the degrees of the vertices of the subgraph in the graph is small. It is known that a plane graph of minimum face size 5 contains light paths and a light pentagon. In this paper we show that every plane graph of minimum face size 5 contains also a light star K1,3 and we present a structural result(More)