In this paper, we present a simple factor 6 algorithm for approximating the optimal multiplicative distortion of embedding a graph metric into a tree metric (thus improving and simplifying the factor 100 and 27 algorithms of Bǎdoiu, Indyk, and Sidiropoulos (2007) and Bǎdoiu, Demaine, Hajiaghayi, Sidiropoulos, and Zadimoghaddam (2008)). We also present a constant factor algorithm for approximati...

Pendidikan profesi dilakukan penilaian pembelajaran melalui student report. Penilaian pada stase mayor dan minor. Pada klinik ditemukan yang tidak terlaksana sesuai kewajiban. Oleh karena itu, peneliti tertarik mengetahui mendeskripsikan kualitas kuantitas Program Studi Profesi Dokter di salah satu Fakultas Kedokteran swasta kota Semarang. Metode menggunakan observasional deskriptif data sekund...

We show that every planar, 4-connected, K2,5-minor-free graph is the square of a cycle of even length at least six.

An irreducibly odd graph is a graph such that each vertex has odd degree and for every pair of vertices, a third vertex in the graph is adjacent to exactly one of the pair. This family of graphs was introduced recently by Manturov [1] in relation to free knots. In this paper, we show that every graph is the induced subgraph of an irreducibly odd graph. Furthermore, we prove that irreducibly odd...

In this note we investigate some matroid minor structure results. In particular, we present sufficient conditions, in terms of triangles, for a matroid to have either U2,4 or F7 or M(K5) as a minor.

A clique-coloring of a given graph G is a coloring of the vertices of G such that no maximal clique of size at least two is monocolored. The clique-chromatic number of G is the least number of colors for which G admits a clique-coloring. It has been proved that every planar graph is 3-clique colorable and every claw-free planar graph, different from an odd cycle, is 2-clique colorable. In this ...

The authors previously published an iterative process to generate a class of projectiveplanarK3,4-free graphs called ‘patch graphs’. They also showed that any simple, almost 4-connected, nonplanar, and projective-planar graph that is K3,4-free is a subgraph of a patch graph. In this paper, we describe a simpler and more natural class of cubic K3,4free projective-planar graphs which we call Möbi...

We show that problems that have finite integer index and satisfy a requirement we call treewidth-bounding admit linear kernels on the class of H-topological-minor free graphs, for an arbitrary fixed graph H . This builds on earlier results by Bodlaender et al. on graphs of bounded genus [2] and by Fomin et al. on H-minor-free graphs [9]. Our framework encompasses several problems, the prominent...