منابع مشابه
The locating-chromatic number for Halin graphs
Let G be a connected graph. Let f be a proper k -coloring of G and Π = (R_1, R_2, . . . , R_k) bean ordered partition of V (G) into color classes. For any vertex v of G, define the color code c_Π(v) of v with respect to Π to be a k -tuple (d(v, R_1), d(v, R_2), . . . , d(v, R_k)), where d(v, R_i) is the min{d(v, x)|x ∈ R_i}. If distinct vertices have distinct color codes, then we call f a locat...
متن کاملMore results on r-inflated graphs: Arboricity, thickness, chromatic number and fractional chromatic number
The r-inflation of a graph G is the lexicographic product G with Kr. A graph is said to have thickness t if its edges can be partitioned into t sets, each of which induces a planar graph, and t is smallest possible. In the setting of the r-inflation of planar graphs, we investigate the generalization of Ringel’s famous Earth-Moon problem: What is the largest chromatic number of any thickness-t ...
متن کاملThe locating chromatic number of the join of graphs
Let $f$ be a proper $k$-coloring of a connected graph $G$ and $Pi=(V_1,V_2,ldots,V_k)$ be an ordered partition of $V(G)$ into the resulting color classes. For a vertex $v$ of $G$, the color code of $v$ with respect to $Pi$ is defined to be the ordered $k$-tuple $c_{{}_Pi}(v)=(d(v,V_1),d(v,V_2),ldots,d(v,V_k))$, where $d(v,V_i)=min{d(v,x):~xin V_i}, 1leq ileq k$. If distinct...
متن کاملThe thickness and chromatic number of r-inflated graphs
A graph has thickness t if the edges can be decomposed into t and no fewer planar layers. We study one aspect of a generalization of Ringel’s famous Earth-Moon problem: what is the largest chromatic number of any thickness-2 graph? In particular, given a graph G we consider the r-inflation of G and find bounds on both the thickness and the chromatic number of the inflated graphs. In some instan...
متن کاملOn complete subgraphs of r-chromatic graphs
Let G,J n) be an r-chromatic graph with n vertices in each colour class . Suppose G = G 3 (n), and t (G) . the minimal degree in G, is at least n + t (t _> 1) . We prove that C contains at least t 3 triangles but does not have to contain more titan 4t 3 of them . Furthermore, we give lower bounds for s such that G contains a complete 3-partite graph with s vertices in each class . Let';.(ii) = ...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2016
ISSN: 0166-218X
DOI: 10.1016/j.dam.2015.07.019