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Bipartite graphs with close domination and k-domination numbers

open access: yesOpen Mathematics, 2020
Let kk be a positive integer and let GG be a graph with vertex set V(G)V(G). A subset D⊆V(G)D\subseteq V(G) is a kk-dominating set if every vertex outside DD is adjacent to at least kk vertices in DD. The kk-domination number γk(G){\gamma }_{k}(G) is the
Ekinci Gülnaz Boruzanlı   +1 more
doaj   +1 more source

Strongly Unichord-Free Graphs

open access: yesDiscussiones Mathematicae Graph Theory, 2019
Several recent papers have investigated unichord-free graphs—the graphs in which no cycle has a unique chord. This paper proposes a concept of strongly unichord-free graph, defined by being unichord-free with no cycle of length 5 or more having exactly ...
McKee Terry A.
doaj   +1 more source

Kaleidoscopic Colorings of Graphs

open access: yesDiscussiones Mathematicae Graph Theory, 2017
For an r-regular graph G, let c : E(G) → [k] = {1, 2, . . . , k}, k ≥ 3, be an edge coloring of G, where every vertex of G is incident with at least one edge of each color.
Chartrand Gary, English Sean, Zhang Ping
doaj   +1 more source

On 3-Coloring of ( 2 P 4 , C 5 )-Free Graphs. [PDF]

open access: yesAlgorithmica, 2022
Jelínek V   +4 more
europepmc   +1 more source

𝒫-Apex Graphs

open access: yesDiscussiones Mathematicae Graph Theory, 2018
Let 𝒫 be an arbitrary class of graphs that is closed under taking induced subgraphs and let 𝒞 (𝒫) be the family of forbidden subgraphs for 𝒫. We investigate the class 𝒫 (k) consisting of all the graphs G for which the removal of no more than k vertices ...
Borowiecki Mieczysław   +2 more
doaj   +1 more source

The {−2,−1}-Selfdual and Decomposable Tournaments

open access: yesDiscussiones Mathematicae Graph Theory, 2018
We only consider finite tournaments. The dual of a tournament is obtained by reversing all the arcs. A tournament is selfdual if it is isomorphic to its dual.
Boudabbous Youssef, Ille Pierre
doaj   +1 more source

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