Tomescu's Graph Coloring Conjecture for $\ell$-Connected Graphs
نویسندگان
چکیده
منابع مشابه
Reducing Hajós’ coloring conjecture to 4-connected graphs
Hajós conjectured that, for any positive integer k, every graph containing no Kk+1-subdivision is k-colorable. This is true when k ≤ 3, and false when k ≥ 6. Hajós’ conjecture remains open for k = 4, 5. In this paper, we show that any possible counterexample to this conjecture for k = 4 with minimum number of vertices must be 4-connected. This is a step in an attempt to reduce Hajós’ conjecture...
متن کامل-λ coloring of graphs and Conjecture Δ ^ 2
For a given graph G, the square of G, denoted by G2, is a graph with the vertex set V(G) such that two vertices are adjacent if and only if the distance of these vertices in G is at most two. A graph G is called squared if there exists some graph H such that G= H2. A function f:V(G) {0,1,2…, k} is called a coloring of G if for every pair of vertices x,yV(G) with d(x,y)=1 we have |f(x)-f(y)|2 an...
متن کاملGraph coloring , perfect graphs 1 Introduction to graph coloring
Let us improve this bound. Assume that G is a connected graph and T is its spanning tree rooted at r. Let us consider an ordering of V (G) in which each vertex v appears after its children in T . Now, for v 6= r we have |N(vi) ∩ {v1, . . . , vi−1}| ≤ deg v − 1, so c(vi) ≤ deg vi for vi 6= r. Unfortunately, the greedy may still need to use ∆(G) + 1 colors if deg r = ∆(G) and each child of r happ...
متن کاملSmall $\ell$-edge-covers in $k$-connected graphs
Let G = (V,E) be a k-edge-connected graph with edge costs {c(e) : e ∈ E} and let 1 ≤ l ≤ k − 1. We show by a simple and short proof, that G contains an l-edge cover I such that: c(I) ≤ l k c(E) if G is bipartite, or if l|V | is even, or if |E| ≥ k|V | 2 + k 2l ; otherwise, c(I) ≤ (
متن کاملconnected graphs cospectral with a friendship graph
let $n$ be any positive integer, the friendship graph $f_n$ consists of $n$ edge-disjoint triangles that all of them meeting in one vertex. a graph $g$ is called cospectral with a graph $h$ if their adjacency matrices have the same eigenvalues. recently in href{http://arxiv.org/pdf/1310.6529v1.pdf}{http://arxiv.org/pdf/1310.6529v1.pdf} it is proved that if $g$ is any graph cospectral with $f_n$...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Discrete Mathematics
سال: 2021
ISSN: 0895-4801,1095-7146
DOI: 10.1137/19m1306646