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輕快走過

Brambles, Prisms and Grids,e their tree-width bounded by an exponential function of .. Using brambles and their well-studied relation to tree-width, we show that they have in fact tree-width .(..). As a consequence, we obtain new bounds on the tree-width of graphs having no small grid as a minor.

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intimate

Ratios of Some Domination Parameters in Graphs and Claw-free Graphs,er, the total domination number, the paired domination number, the double domination number and the independence number. We summarize the old and new results in a table and give for each bound examples of extremal families.

Vulvodynia

Excessive Factorizations of Regular Graphs,egular graphs. We introduce two graph parameters related to excessive factorizations and show that their computation is NP-hard. We pose a number of questions regarding these parameters. We show that the size of an excessive factorization of a regular graph can exceed the degree of the graph by an a

Anthrp

北極熊

On Edge-maps whose Inverse Preserves Flows or Tensions, . if the pre-image of every cycle of . is a cycle of .. A fascinating conjecture of Jaeger asserts that every bridgeless graph has a cycle-continuous mapping to the Petersen graph. Jaeger showed that if this conjecture is true, then so is the 5-cycle-double-cover conjecture and the Fulkerson conjec

無脊椎

hurricane

Even Pairs in Bull-reducible Graphs,rtices such that every chordless path joining them has even length. We prove that for every bull-reducible Berge graph . with at least two vertices, either . or its complementary graph . has an even pair.

Corral

Kernels in Orientations of Pretransitive Orientable Graphs,h that for every . ∈ . (.) ? . there exists an arc from . to .. A digraph . is called . (resp. left-pretransitive) when (.) ∈ .(.) and (.) ∈ .(.) implies (.) ∈ .(.) or (.) ∈ .(.) (resp. (.) ∈ .(.) and (.) ∈ .(.) implies (.) ∈ .(.) or (.) ∈ .(.)). These concepts were introduced by P. Duchet in 1980.

Fsh238

Nonrepetitive Graph Coloring,r a graph . is denoted by π(.). For instance, by the famous 1906 theorem of Thue, π(.) = 3 if . is a simple path with at least 4 vertices. This implies that π(.) ≤ 4 if Δ(.) ≤ 2. But how large can π(.) be for cubic graphs, .-trees, or planar graphs? This paper is a small survey of problems and resul