نتایج جستجو برای: 3 free graph
تعداد نتایج: 2382585 فیلتر نتایج به سال:
A graph G has the hourglass property if every induced hourglass S (a tree with a degree sequence 22224) contains two non-adjacent vertices which have a common neighbor in G − V (S). For an integer k ≥ 4, a graph G has the single k-cycle property if every edge of G, which does not lie in a triangle, lies in a cycle C of order at most k such that C has at least |V (C)| 2 edges which do not lie in...
A graph G is k-choosable if for every assignment of a set S(v) of k colors to every vertex v of G, there is a proper coloring of G that assigns to each vertex v a color from S(v). We consider the complexity of deciding whether a given graph is k-choosable for some constant k. In particular, it is shown that deciding whether a given planar graph is 4-choosable is NP-hard, and so is the problem o...
A hole in a graph is an induced subgraph which is a cycle of length at least four. We prove that for all ν > 0, every triangle-free graph with sufficiently large chromatic number contains holes of ν consecutive lengths. In particular, this implies two well-known conjectures of Gyárfás [3], namely that every triangle-free graph with sufficiently large chromatic number has a hole of length at lea...
We give a linear-time algorithm to decide 3-colorability of triangle-free graph embedded in fixed surface, and quadratic-time output 3-coloring the affirmative case. The algorithms also allow prescribe coloring bounded number vertices.
The k-Coloring problem is to test whether a graph can be colored with at most k colors such that no two adjacent vertices receive the same color. If a graph G does not contain a graph H as an induced subgraph, then G is called H-free. For any fixed graph H on at most 6 vertices, it is known that 3-Coloring is polynomial-time solvable on H-free graphs whenever H is a linear forest and NP-complet...
A graph G is Nm-locally connected if for every vertex v in G, the vertices not equal to v and with distance at most m to v induce a connected subgraph in G. We show that both connectedN2-locally connected claw-free graph and 3-edge-connected N3-locally connected claw-free graph have connected even [2, 4]-factors, which settle a conjecture by Li in [6].
A graph G is k-choosable if for every assignment of a set S(v) of k colors to every vertex v of G, there is a proper coloring of G that assigns to each vertex v a color from S(v). We consider the complexity of deciding whether a given graph is k-choosable for some constant k. In particular, it is shown that deciding whether a given planar graph is 4-choosable is NP-hard, and so is the problem o...
An acyclic edge coloring of a graph is a proper edge coloring such that there are no bichromatic cycles. The acyclic chromatic index of a graph is the minimum number k such that there is an acyclic edge coloring using k colors and is denoted by a(G). It was conjectured by Alon, Sudakov and Zaks (and much earlier by Fiamcik) that a(G) ≤ ∆ + 2, where ∆ = ∆(G) denotes the maximum degree of the gra...
A graph G is Nm-locally connected if for every vertex v in G, the vertices not equal to v and with distance at most m to v induce a connected subgraph in G. We show that both connected N2-locally connected claw-free graph and 3-edge-connected N3-locally connected claw-free graph have connected even [2, 4]-factors, which settle a conjecture by Li in [6].
A finite simple graph Γ is called a Nest if it regular of valency 6 and admits an automorphism ρ with two orbits the same length such that at least one subgraphs induced by these cycle. We say core-free no non-trivial subgroup group generated normal in Aut(Γ). In this paper, we show that, edge-transitive core-free, then isomorphic to following graphs: complement Petersen graph, Hamming H(2,4), ...
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