Results 41 to 50 of about 168,763 (311)
The complexity of two graph orientation problems
, 2012 This is the post-print version of the Article. The official published version can be accessed from the link below - Copyright @ 2012 ElsevierWe consider two orientation problems in a graph, namely the minimization of the sum of all the shortest path ...
Noble, Steven D. +7 more
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Coloring graphs with forbidden minors
Journal of Combinatorial Theory, Series B, 2017 Hadwiger's conjecture from 1943 states that for every integer $t\ge1$, every graph either can be $t$-colored or has a subgraph that can be contracted to the complete graph on $t+1$ vertices. As pointed out by Paul Seymour in his recent survey on Hadwiger's conjecture, proving that graphs with no $K_7$ minor are $6$-colorable is the first case of ...
Martin Rolek, Zi-Xia Song
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Minimizing the oriented diameter of a planar graph
, 2009 We consider the problem of minimizing the diameter of an orientation of a planar graph. A result of Chvátal and Thomassen shows that for general graphs, it is NP-complete to decide whether a graph can be oriented so that its diameter is at most two.
Noble, SD +3 more
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Grid Minors of Graphs on the Torus
Journal of Combinatorial Theory, Series B, 1994 The face-width of a graph embedded on the torus is the smallest \(n\) such that there is a noncontractible cycle on the torus which intersects the graph in exactly \(n\) points. For example, the product of two \(n\)-cycles \(C_ n\times C_ n\) embeds on the torus with face-width \(n\); this embedding is called the toroidal \(n\)-grid. A graph \(H\) is a
de Graaf, M., Schrijver, A.
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Graphs with no $\bar P_7$-Minor [PDF]
The Electronic Journal of Combinatorics, 2016 Let $\bar P_7$ denote the complement of a path on seven vertices. We determine all 4-connected graphs that do not contain $\bar P_7$ as a minor.
Guoli Ding +2 more
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The Liouville and the intersection properties are equivalent for planar graphs [PDF]
, 2012 It is shown that if a planar graph admits no non-constant bounded harmonic function then the trajectories of two independent simple random walks intersect almost ...
Itai Benjamini +5 more
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Clique Minors in Graphs and Their Complements
Journal of Combinatorial Theory, Series B, 2000 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bruce A. Reed, Robin Thomas 0001
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Every infinitely edge-connected graph contains the Farey graph or Tℵ0 ∗ t as a minor [PDF]
, 2022 We show that every infinitely edge-connected graph contains the Farey graph or Tℵ0 ∗ t as a minor.
Kurkofka, Jan
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Faster parameterized algorithms for modification problems to minor-closed classes [PDF]
TheoretiCSLet ${\cal G}$ be a minor-closed graph class and let $G$ be an $n$-vertex graph. We say that $G$ is a $k$-apex of ${\cal G}$ if $G$ contains a set $S$ of at most $k$ vertices such that $G\setminus S$ belongs to ${\cal G}$.
Laure Morelle +3 more
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Rectilinear Crossing Number of Graphs Excluding a Single-Crossing Graph as a Minor [PDF]
The rectilinear crossing number of G is the minimum number of crossings in a straight-line drawing of G. A single-crossing graph is a graph whose crossing number is at most one.
Dujmović, Vida, La Rose, Camille
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