Temat: Total graph - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Edge colorings and total colorings of integer distance graphs
Autorzy:: Kemnitz, Arnfried
Marangio, Massimiliano
Powiązania:: https://bibliotekanauki.pl/articles/743555.pdf
Data publikacji:: 2002
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: integer distance graph
chromatic number
choice number
chromatic index
choice index
total chromatic number
total choice number
Opis:: An integer distance graph is a graph G(D) with the set Z of integers as vertex set and two vertices u,v ∈ Z are adjacent if and only if |u-v| ∈ D where the distance set D is a subset of the positive integers N. In this note we determine the chromatic index, the choice index, the total chromatic number and the total choice number of all integer distance graphs, and the choice number of special integer distance graphs.
Źródło:: Discussiones Mathematicae Graph Theory; 2002, 22, 1; 149-158
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 2.

Tytuł:: Generalized Fractional and Circular Total Colorings of Graphs
Autorzy:: Kemnitz, Arnfried
Marangio, Massimiliano
Mihók, Peter
Oravcová, Janka
Soták, Roman
Powiązania:: https://bibliotekanauki.pl/articles/31339338.pdf
Data publikacji:: 2015-08-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: graph property
(P,Q)-total coloring
circular coloring
fractional coloring
fractional (P,Q)-total chromatic number
circular (P,Q)- total chromatic number
Opis:: Let $ \mathcal{P} $ and $ \mathcal{Q} $ be additive and hereditary graph properties, $ r, s \in \mathbb{N}$, $ r \ge s $, and $ [\mathbb{Z}_r]^s $ be the set of all s-element subsets of $\mathbb{Z}_r $. An ($r$, $s$)-fractional ($ \mathcal{P} $,$ \mathcal{Q} $)-total coloring of $G$ is an assignment $ h : V (G) \cup E(G) \rightarrow [\mathbb{Z}_r]^s $ such that for each $ i \in \mathbb{Z}_r $ the following holds: the vertices of $G$ whose color sets contain color $i$ induce a subgraph of $G$ with property $ \mathcal{P} $, edges with color sets containing color $i$ induce a subgraph of $G$ with property $ \mathcal{Q} $, and the color sets of incident vertices and edges are disjoint. If each vertex and edge of $G$ is colored with a set of $s$ consecutive elements of $ \mathbb{Z}_r $ we obtain an ($r$, $s$)-circular ($ \mathcal{P} $,$ \mathcal{Q} $)-total coloring of $G$. In this paper we present basic results on ($r$, $s$)-fractional/circular ($ \mathcal{P} $,$ \mathcal{Q} $)-total colorings. We introduce the fractional and circular ($ \mathcal{P} $,$ \mathcal{Q}$)-total chromatic number of a graph and we determine this number for complete graphs and some classes of additive and hereditary properties.
Źródło:: Discussiones Mathematicae Graph Theory; 2015, 35, 3; 517-532
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 3.

Tytuł:: Fractional ($ \mathcal{P} , \mathcal{Q} $)-Total List Colorings of Graphs
Autorzy:: Kemnitz, Arnfried
Mihók, Peter
Voigt, Margit
Powiązania:: https://bibliotekanauki.pl/articles/30146708.pdf
Data publikacji:: 2013-03-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: graph property
total coloring
(P,Q)-total coloring
fractional coloring
fractional (P,Q)-total chromatic number
circular coloring
circular (P,Q)-total chromatic number
list coloring
(P,Q)-total (a
b)-list colorings
Opis:: Let $ r, s \in \mathbb{N}$, $r \ge s$, and $ \mathcal{P} $ and $ \mathcal{Q} $ be two additive and hereditary graph properties. A $ (P,Q) $-total $(r, s)$-coloring of a graph $G = (V,E)$ is a coloring of the vertices and edges of $G$ by $s$-element subsets of $ \mathbb{Z}_r$ such that for each color $i$, $0 \le i \le r − 1$, the vertices colored by subsets containing $i$ induce a subgraph of $G$ with property $ \mathcal{P} $, the edges colored by subsets containing $i$ induce a subgraph of $G$ with property $ \mathcal{Q} $, and color sets of incident vertices and edges are disjoint. The fractional $ (\mathcal{P}, \mathcal{Q})$-total chromatic number $ \chi_{f,P,Q}^{''}(G)$ of $G$ is defined as the infimum of all ratios $r//s$ such that $G$ has a $ ( \mathcal{P}, \mathcal{Q})$-total $(r, s)$-coloring. A $ ( \mathcal{P}, \mathcal{Q} $-total independent set $ T = V_T \cup E_T \subseteq V \cup E$ is the union of a set $V_T$ of vertices and a set $E_T$ of edges of $G$ such that for the graphs induced by the sets $V_T$ and $E_T$ it holds that $ G[ V_T ] \in \mathcal{ P } $, $ G[ E_T ] \in \mathcal{Q} $, and $ G[ V_T ] $ and $ G[ E_T ] $ are disjoint. Let $ T_{ \mathcal{P} , \mathcal{Q} } $ be the set of all $ (\mathcal{P} ,\mathcal{Q})$-total independent sets of $G$. Let $L(x)$ be a set of admissible colors for every element $ x \in V \cup E $. The graph $G$ is called $ (\mathcal{P} , \mathcal{Q}) $-total $(a, b)$-list colorable if for each list assignment $L$ with $|L(x)| = a$ for all $x \in V \cup E$ it is possible to choose a subset $ C(x) \subseteq L(x)$ with $|C(x)| = b$ for all $ x \in V \cup E$ such that the set $ T_i $ which is defined by $ T_i = {x \in V \cup E : i \in C(x) } $ belongs to $ T_{ \mathcal{P},\mathcal{Q}}$ for every color $i$. The $ (\mathcal{P}, \mathcal{Q})$- choice ratio $ \text{chr}_{\mathcal{P},\mathcal{Q}}(G)$ of $G$ is defined as the infimum of all ratios $a//b$ such that $G$ is $ (\mathcal{P},\mathcal{Q})$-total $(a, b)$-list colorable. We give a direct proof of $ \chi_{ f,\mathcal{P},\mathcal{Q} }^{ \prime \prime } (G) = \text{chr}_{ \mathcal{P} ,\mathcal{Q} }(G)$ for all simple graphs $G$ and we present for some properties $ \mathcal{P} $ and $ \mathcal{Q} $ new bounds for the $ (\mathcal{P}, \mathcal{Q})$-total chromatic number and for the $(\mathcal{P},\mathcal{Q})$-choice ratio of a graph $G$.
Źródło:: Discussiones Mathematicae Graph Theory; 2013, 33, 1; 167-179
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

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