Results 11 to 20 of about 1,022,735 (236)
Remarks on path-factor critical avoidable graphs
International Journal of Cognitive Computing in Engineering, 2023 Zhou (2023) introduced the concept of path-factor critical avoidable graph and determined several parameter bounds for (P≥2,n) or (P≥3,n)-factor critical avoidable graphs.
Zhengyue He +3 more
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Distinguishing critical graphs [PDF]
Journal of Information and Optimization Sciences, 2020 The distinguishing number $D(G)$ of a graph $G$ is the least integer $d$ such that $G$ has a vertex labeling with $d$ labels that is preserved only by a trivial automorphism. We say that a graph $G$ is $d$-distinguishing critical, if $D(G)=d$ and $D(H)\neq D(G)$, for every proper induced subgraph $H$ of $G$.
Alikhani, Saeid, Soltani, Samaneh
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Structural Properties of Connected Domination Critical Graphs
Mathematics, 2021 A graph G is said to be k-γc-critical if the connected domination number γc(G) is equal to k and γc(G+uv)
Norah Almalki, Pawaton Kaemawichanurat
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Domination Critical Knödel Graphs [PDF]
Iranian Journal of Science and Technology, Transactions A: Science, 2019 A set $D$ of vertices of a graph $G$ is a dominating set if each vertex of $V(G)\setminus D$ is adjacent to some vertex of $D$. The domination number of $G$, $ (G)$, is the minimum cardinality of a dominating set of $G$. A graph $G$ is called domination vertex critical, or just $ $-critical if removal of any vertex decreases the domination number.
D. A. Mojdeh, S. R. Musawi, E. Nazari
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Equimatchable Bipartite Graphs
Discussiones Mathematicae Graph Theory, 2023 A graph is called equimatchable if all of its maximal matchings have the same size. Lesk et al. [Equi-matchable graphs, Graph Theory and Combinatorics (Academic Press, London, 1984) 239–254] has provided a characterization of equimatchable bipartite ...
Büyükçolak Yasemin +2 more
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Graphs that are Critical for the Packing Chromatic Number
Discussiones Mathematicae Graph Theory, 2022 Given a graph G, a coloring c : V (G) → {1, …, k} such that c(u) = c(v) = i implies that vertices u and v are at distance greater than i, is called a packing coloring of G.
Brešar Boštjan, Ferme Jasmina
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Cycles in Color-Critical Graphs [PDF]
The Electronic Journal of Combinatorics, 2021 Tuza [1992] proved that a graph with no cycles of length congruent to $1$ modulo $k$ is $k$-colorable. We prove that if a graph $G$ has an edge $e$ such that $G-e$ is $k$-colorable and $G$ is not, then for $2\le r\le k$, the edge $e$ lies in at least $\prod_{i=1}^{r-1} (k-i)$ cycles of length $1\mod r$ in $G$, and $G-e$ contains at least $\frac12 ...
Moore, Benjamin R., West, Douglas B.
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On vertex b-critical trees [PDF]
Opuscula Mathematica, 2013 A b-coloring is a proper coloring of the vertices of a graph such that each color class has a vertex that has neighbors of all other colors. The b-chromatic number of a graph G is the largest k such that G admits a b-coloring with k colors.
Mostafa Blidia +2 more
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Exhaustive generation of $k$-critical $\mathcal H$-free graphs [PDF]
, 2015 We describe an algorithm for generating all $k$-critical $\mathcal H$-free graphs, based on a method of Ho\`{a}ng et al. Using this algorithm, we prove that there are only finitely many $4$-critical $(P_7,C_k)$-free graphs, for both $k=4$ and $k=5$.
B Randerath +17 more
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