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Traceability in ${K_{1, 4}, K_{1, 4} + e}$ -free graphs

Wei Zheng; Ligong Wang — 2019

Czechoslovak Mathematical Journal

A graph $G$ is called ${H_{1}, H_{2}, \dots, H_{k}}$ -free if $G$ contains no induced subgraph isomorphic to any graph $H_{i}$ , $1 \leq i \leq k$ . We define $σ_{k} = min \{\sum_{i = 1}^{k} d (v_{i}) : {v_{1}, \dots, v_{k}} is an independent set of vertices in G\} .$ In this paper, we prove that (1) if $G$ is a connected ${K_{1, 4}, K_{1, 4} + e}$ -free graph of order $n$ and $σ_{3} (G) \geq n - 1$ , then $G$ is traceable, (2) if $G$ is a 2-connected ${K_{1, 4}, K_{1, 4} + e}$ -free graph of order $n$ and $| N (x_{1}) \cup N (x_{2}) | + | N (y_{1}) \cup N (y_{2}) | \geq n - 1$ for any two distinct pairs of non-adjacent vertices ${x_{1}, x_{2}}$ , ${y_{1}, y_{2}}$ of $G$ , then $G$ is traceable, i.e., $G$ has a Hamilton path, where $K_{1, 4} + e$ is a graph obtained by joining a pair of non-adjacent vertices in a $K_{1, 4}$ .

Division schemes under uncertainty of claims

Xianghui Li; Yang Li; Wei Zheng — 2021

Kybernetika

In some economic or social division problems, we may encounter uncertainty of claims, that is, a certain amount of estate has to be divided among some claimants who have individual claims on the estate, and the corresponding claim of each claimant can vary within a closed interval or fuzzy interval. In this paper, we classify the division problems under uncertainty of claims into three subclasses and present several division schemes from the perspective of axiomatizations, which are consistent with...

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Currently displaying 1 – 14 of 14

Traceability in ${K_{1, 4}, K_{1, 4} + e}$ -free graphs

Division schemes under uncertainty of claims

Semimartingales in predictable random open sets

Une remarque sur une même i.s. calculée dans deux filtrations

Meyer's topology and brownian motion in a composite medium

Adaptive algorithm for noisy autoregressive signals.

Study of a least-squares-based algorithm for autoregressive signals subject to white noise.

Sur la construction de certaines diffusions

Intégrales stochastiques non monotones

Remarques sur la convergence des martingales dans les variétés

Fonctions convexes et semimartingales dans une variété

Quelques résultats de « mécanique stochastique »

Construction de processus de Nelson réversibles

Sur la convergence des semimartingales continues dans $ℝ^{n}$ et des martingales dans une variété