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pro vyhledávání: '"05C15, 05C69"'
Two relationships between the injective chromatic number and, respectively, chromatic number and chromatic index, are proved. They are applied to determine the injective chromatic number of Sierpi\'nski graphs and to give a short proof that Sierpi\'n
Externí odkaz:
http://arxiv.org/abs/2409.08856
Autor:
George, Phebe Sarah, Naduvath, Sudev
A proper vertex coloring of the graph $G$ such that each vertex dominates at least one color class and the cardinalities of the color classes differ by at most $1$ is called an equitable dominator coloring of $G$. The minimum number of colors used in
Externí odkaz:
http://arxiv.org/abs/2408.14382
This paper introduces a new variant of domination-related coloring of graphs, which is a combination of their dominator coloring and equitable coloring called the equitable dominator coloring. An equitable coloring is a proper coloring in which the n
Externí odkaz:
http://arxiv.org/abs/2408.14374
Given a graph $G$, a mutual-visibility coloring of $G$ is introduced as follows. We color two vertices $x,y\in V(G)$ with a same color, if there is a shortest $x,y$-path whose internal vertices have different colors than $x,y$. The smallest number of
Externí odkaz:
http://arxiv.org/abs/2408.03132
Autor:
Steiner, Raphael
The cochromatic number $\zeta(G)$ of a graph $G$ is the smallest number of colors in a vertex-coloring of $G$ such that every color class forms an independent set or a clique. In three papers written around 1990, Erd\H{o}s, Gimbel and collaborators r
Externí odkaz:
http://arxiv.org/abs/2408.02400
Autor:
Dejter, Italo J.
Let $2\le k\in\mathbb{Z}$. A total coloring of a $k$-regular simple graph via $k+1$ colors is an {\it efficient total coloring} if each color class is an efficient dominating set, where the efficient domination condition applies to the restriction of
Externí odkaz:
http://arxiv.org/abs/2405.08781
We work with simple graphs in ZF (Zermelo--Fraenkel set theory without the Axiom of Choice (AC)) and assume that the sets of colors can be either well-orderable or non-well-orderable to prove that the following statements are equivalent to K\H{o}nig
Externí odkaz:
http://arxiv.org/abs/2309.06116
In the inhomogeneous random graph model, each vertex $i\in\{1,\ldots,n\}$ is assigned a weight $W_i\sim\text{Unif}(0,1)$, and an edge between any two vertices $i,j$ is present with probability $k(W_i,W_j)/\lambda_n\in[0,1]$, where $k$ is a positive,
Externí odkaz:
http://arxiv.org/abs/2306.06396
Publikováno v:
Bulletin of the Malaysian Mathematical Sciences Society, 2024
The problem of injective coloring in graphs can be revisited through two different approaches: coloring the two-step graphs and vertex partitioning of graphs into open packing sets, each of which is equivalent to the injective coloring problem itself
Externí odkaz:
http://arxiv.org/abs/2306.01488
A partition $\pi=\{V_{1},V_{2},...,V_{k}\}$ of the vertex set $V$ of a graph $G$ into $k$ color classes $V_{i}$, with $1\leq i\leq k$ is called a quorum coloring of $G$ if for every vertex $v\in V$, at least half of the vertices in the closed neighbo
Externí odkaz:
http://arxiv.org/abs/2305.03585