منابع مشابه
Cliques, minors and apex graphs
In this paper, we proved the following result: Let G be a (k + 2)-connected, non-(k − 3)apex graph where k ≥ 2. If G contains three k-cliques, say L1, L2, L3, such that |Li ∩ Lj| ≤ k − 2(1 ≤ i < j ≤ 3), then G contains a Kk+2 as a minor. Note that a graph G is t-apex if G− X is planar for some subset X ⊆ V (G) of order at most t . This theorem generalizes some earlier results by Robertson, Seym...
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A graph H is t-apex if H − X is planar for some set X ⊂ V (H) of size t. For any integer t ≥ 0 and a fixed t-apex graph H, we give a polynomial-time algorithm to decide whether a (t + 3)-connected Hminor-free graph is colorable from a given assignment of lists of size t+4. The connectivity requirement is the best possible in the sense that for every t ≥ 1, there exists a t-apex graph H such tha...
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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v Chapter 1: Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Graph Mino...
متن کاملThe p-median and p-center Problems on Bipartite Graphs
Let $G$ be a bipartite graph. In this paper we consider the two kind of location problems namely $p$-center and $p$-median problems on bipartite graphs. The $p$-center and $p$-median problems asks to find a subset of vertices of cardinality $p$, so that respectively the maximum and sum of the distances from this set to all other vertices in $G$ is minimized. For each case we present some proper...
متن کاملFace Covers and the Genus of Apex Graphs
A graph G is an apex graph if it contains a vertex w such that G w is a planar graph It is easy to see that the genus g G of the apex graph G is bounded above by where is the minimum face cover of the neighbors of w taken over all planar embeddings of G w The main result of this paper is the linear lower bound g G if G w is connected and It is also proved that computing the genus of apex graphs...
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ژورنال
عنوان ژورنال: Discussiones Mathematicae Graph Theory
سال: 2018
ISSN: 1234-3099,2083-5892
DOI: 10.7151/dmgt.2041