Critical (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e178" altimg="si9.svg"><mml:msub><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mn>5</mml:mn></mml:mrow></mml:msub></mml:math>, bull)-free graphs
نویسندگان
چکیده
Given two graphs H1 and H2, a graph is (H1,H2)-free if it contains no induced subgraph isomorphic to or H2. Let Pt be the path on t vertices. A bull obtained from triangle with disjoint pendant edges. In this paper, we show that there are finitely many 5-vertex-critical (P5, bull)-free graphs.
منابع مشابه
Optimizing Bull-Free Perfect Graphs
A bull is a graph obtained by adding a pendant vertex at two vertices of a triangle. Here we present polynomial-time combinatorial algorithms for the optimal weighted coloring and weighted clique problems in bull-free perfect graphs. The algorithms are based on a structural analysis and decomposition of bull-free perfect graphs.
متن کاملColoring ($P_5$, bull)-free graphs
We give a polynomial-time algorithm that computes the chromatic number of any graph that contains no path on five vertices and no bull as an induced subgraph (where the bull is the graph with five vertices a, b, c, d, e and edges ab, bc, cd, be, ce).
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The bull is a graph consisting of a triangle and two vertex-disjoint pendant edges. A graph is called bull-free if no induced subgraph of it is a bull. A graph G is perfect if for every induced subgraph H of G, the chromatic number of H equals the size of the largest complete subgraph of H. This paper describes the structure of all bull-free perfect graphs.
متن کاملOdd holes in bull-free graphs
The complexity of testing whether a graph contains an induced odd cycle of length at least five is currently unknown. In this paper we show that this can be done in polynomial time if the input graph has no induced subgraph isomorphic to the bull (a triangle with two disjoint pendant edges).
متن کاملThe structure of bull-free graphs II — elementary trigraphs
The bull is a graph consisting of a triangle and two pendant edges. A graph is called bull-free if no induced subgraph of it is a bull. This is the second paper in a series of three. The goal of the series is to give a complete description of all bull-free graphs. We call a bull-free graph elementary if it does not contain an induced three-edge-path P such that some vertex c 6∈ V (P ) is comple...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2023
ISSN: ['1872-6771', '0166-218X']
DOI: https://doi.org/10.1016/j.dam.2023.02.019