Autor: Lih, Ko-Wei - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Upper Bounds for the Strong Chromatic Index of Halin Graphs
Autorzy:: Hu, Ziyu
Lih, Ko-Wei
Liu, Daphne Der-Fen
Powiązania:: https://bibliotekanauki.pl/articles/16647759.pdf
Data publikacji:: 2018-02-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: strong edge-coloring
strong chromatic index
Halin graphs
Opis:: The strong chromatic index of a graph G, denoted by χ′s(G), is the minimum number of vertex induced matchings needed to partition the edge set of G. Let T be a tree without vertices of degree 2 and have at least one vertex of degree greater than 2. We construct a Halin graph G by drawing T on the plane and then drawing a cycle C connecting all its leaves in such a way that C forms the boundary of the unbounded face. We call T the characteristic tree of G. Let G denote a Halin graph with maximum degree Δ and characteristic tree T. We prove that χ′s(G) ⩽ 2Δ + 1 when Δ ⩾ 4. In addition, we show that if Δ = 4 and G is not a wheel, then χ′s(G) ⩽ χ′s(T) + 2. A similar result for Δ = 3 was established by Lih and Liu [21].
Źródło:: Discussiones Mathematicae Graph Theory; 2018, 38, 1; 5-26
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: Upper Bounds for the Strong Chromatic Index of Halin Graphs
Autorzy:: Hu, Ziyu
Lih, Ko-Wei
Liu, Daphne Der-Fen
Powiązania:: https://bibliotekanauki.pl/articles/31342445.pdf
Data publikacji:: 2018-02-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: strong edge-coloring
strong chromatic index
Halin graphs
Opis:: The strong chromatic index of a graph $G$, denoted by $ \chi_s^′ (G) $, is the minimum number of vertex induced matchings needed to partition the edge set of $G$. Let $T$ be a tree without vertices of degree 2 and have at least one vertex of degree greater than 2. We construct a Halin graph $G$ by drawing $T$ on the plane and then drawing a cycle $C$ connecting all its leaves in such a way that $C$ forms the boundary of the unbounded face. We call $T$ the characteristic tree of $G$. Let $G$ denote a Halin graph with maximum degree $ \Delta $ and characteristic tree $T$. We prove that $ \chi_s^′ (G) \le 2 \Delta + 1 $ when $ \Delta \ge 4 $. In addition, we show that if $ \Delta = 4 $ and $G$ is not a wheel, then $ \chi_s^′ (G) \le \chi_s^′ (T) + 2 $. A similar result for $ \Delta = 3 $ was established by Lih and Liu [21].
Źródło:: Discussiones Mathematicae Graph Theory; 2018, 38, 1; 5-26
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 3.

Tytuł:: Adjacent vertex distinguishing edge-colorings of planar graphs with girth at least six
Autorzy:: Bu, Yuehua
Lih, Ko-Wei
Wang, Weifan
Powiązania:: https://bibliotekanauki.pl/articles/743930.pdf
Data publikacji:: 2011
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: edge-coloring
vertex-distinguishing
planar graph
Opis:: An adjacent vertex distinguishing edge-coloring of a graph G is a proper edge-coloring o G such that any pair of adjacent vertices are incident to distinct sets of colors. The minimum number of colors required for an adjacent vertex distinguishing edge-coloring of G is denoted by χ'ₐ(G). We prove that χ'ₐ(G) is at most the maximum degree plus 2 if G is a planar graph without isolated edges whose girth is at least 6. This gives new evidence to a conjecture proposed in [Z. Zhang, L. Liu, and J. Wang, Adjacent strong edge coloring of graphs, Appl. Math. Lett., 15 (2002) 623-626.]
Źródło:: Discussiones Mathematicae Graph Theory; 2011, 31, 3; 429-439
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

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