نتایج جستجو برای: free graph

تعداد نتایج: 699741  

amin Naseri elips masehian

In this paper, a new online robot motion planner is developed for systematically exploring unknown environ¬ments by intelligent mobile robots in real-time applications. The algorithm takes advantage of sensory data to find an obstacle-free start-to-goal path. It does so by online calculation of the Generalized Voronoi Graph (GVG) of the free space, and utilizing a combination of depth-first an...

Journal: :Journal of Graph Theory 2014
Zdenek Ryjácek Petr Vrána

A graph G is 1-Hamilton-connected if G − x is Hamilton-connected for every vertex x ∈ V (G). In the paper we introduce a closure concept for 1-Hamiltonconnectedness in claw-free graphs. If G is a (new) closure of a claw-free graph G, then G is 1-Hamilton-connected if and only if G is 1-Hamilton-connected, G is the line graph of a multigraph, and for some x ∈ V (G), G − x is the line graph of a ...

Journal: :CoRR 2013
Weisheng Si

Greedy Forwarding algorithm is a widely-used routing algorithm for wireless networks. However, it can fail if the wireless network topologies contain void scenarios (or simply called voids). Since Yao Graph and Theta Graph are two types of geometric graphs exploited to construct wireless network topologies, this paper studies whether these two types of graphs can contain voids. Specifically, th...

Journal: :Discrete Mathematics 2011
Jun Fujisawa Katsuhiro Ota Kenta Ozeki Gabriel Sueiro

Let H be a family of connected graphs. A graph G is said to be H-free if G is H-free for every graph H in H. In [1] it was pointed that there is a family of connected graphs H not containing any induced subgraph of the claw having the property that the set of H-free connected graphs containing a claw is finite, provided also that those graphs have minimum degree at least two and maximum degree ...

Journal: :Discrete Applied Mathematics 2016
Nathan Kahl

Let τ(G) and τG(e) denote the number of spanning trees of a graph G and the number of spanning trees of G containing edge e of G, respectively. Ferrara, Gould, and Suffel asked if, for every rational 0 < p/q < 1 there existed a graph G with edge e ∈ E(G) such that τG(e)/τ(G) = p/q. In this note we provide constructions that show this is indeed the case. Moreover, we show this is true even if we...

Journal: :Discrete Mathematics 2009
Timothy J. Hetherington

It is proved that if G is a plane embedding of a K4-minor-free graph with maximum degree ∆, then G is entirely 7-choosable if ∆ ≤ 4 and G is entirely (∆+2)-choosable if ∆ ≥ 5; that is, if every vertex, edge and face of G is given a list of max{7,∆+2} colours, then every element can be given a colour from its list such that no two adjacent or incident elements are given the same colour. It is pr...

2005
Maria Chudnovsky Paul D. Seymour

A graph is claw-free if no vertex has three pairwise nonadjacent neighbours. At first sight, there seem to be a great variety of types of claw-free graphs. For instance, there are line graphs, the graph of the icosahedron, complements of triangle-free graphs, and the Schläfli graph (an amazingly highly-symmetric graph with 27 vertices), and more; for instance, if we arrange vertices in a circle...

Journal: :Discrete Mathematics 2015
Kenta Ozeki Zdenek Ryjácek Kiyoshi Yoshimoto

In this paper, we show that every 3-connected claw-free graph G has a 2-factor having at most max { 2 5(α+1), 1 } cycles, where α is the independence number of G. As a corollary of this result, we also prove that every 3-connected claw-free graph G has a 2-factor with at most ( 4|G| 5(δ+2)+ 2 5 ) cycles, where δ is the minimum degree of G. This is an extension of a known result on the number of...

2013
Maria Chudnovsky Alexandra Fradkin Matthieu Plumettaz

In 1968, Erdös and Lovász conjectured that for every graph G and all integers s, t ≥ 2 such that s + t − 1 = χ(G) > ω(G), there exists a partition (S, T ) of the vertex set of G such that χ(G|S) ≥ s and χ(G|T ) ≥ t. For general graphs, the only settled cases of the conjecture are when s and t are small. Recently, the conjecture was proved for a few special classes of graphs: graphs with stabili...

Journal: :Journal of Graph Theory 1996
Armen S. Asratian

A graph G is locally connected if the subgraph induced by the neighbourhood of each vertex is connected. We prove that a locally connected graph G of order p 3, containing no induced subgraph isomorphic to K 1;3 , is Hamilton-connected if and only if G is 3-connected.

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